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    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019bdcae-e261-7fc2-8943-5f5b8b5f27bc_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_019bdcae-e261-7a2f-9c12-e9f00adcd499_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held to maturity:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_019bdcae-e260-71c4-a14b-df5ec1f2ef93_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_019bdcae-e2e9-7be8-b56a-fcaf405ba68b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on preferred stock</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Preferred Stock and Preference Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:to="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery_019bdcae-e2e9-7b91-a6b9-b883219d9117_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoveries</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Recovery</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_019bdcae-e261-7110-90c6-f66483510639_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:to="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss_019bdcae-e2e9-7e56-be52-0c6147cc4bf5_negatedLabel_en-US" xlink:label="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for Other Real Estate Owned losses</link:label>
    <link:label id="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss_label_en-US" xlink:label="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate, Foreclosed Assets, and Repossessed Assets, Allowance For Credit Loss</link:label>
    <link:label id="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Real Estate, Foreclosed Assets, and Repossessed Assets, Allowance For Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:href="fgbi-20251231.xsd#fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:to="lab_fgbi_OtherRealEstateForeclosedAssetsAndRepossessedAssetsAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AgriculturalMember_019bdcae-e261-743b-9759-6381d27f5755_terseLabel_en-US" xlink:label="lab_fgbi_AgriculturalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agricultural</link:label>
    <link:label id="lab_fgbi_AgriculturalMember_019bdcae-e261-7c13-9afd-04ea66385403_verboseLabel_en-US" xlink:label="lab_fgbi_AgriculturalMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Agricultural</link:label>
    <link:label id="lab_fgbi_AgriculturalMember_label_en-US" xlink:label="lab_fgbi_AgriculturalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agricultural [Member]</link:label>
    <link:label id="lab_fgbi_AgriculturalMember_documentation_en-US" xlink:label="lab_fgbi_AgriculturalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the operations of agricultural activities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AgriculturalMember" xlink:href="fgbi-20251231.xsd#fgbi_AgriculturalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AgriculturalMember" xlink:to="lab_fgbi_AgriculturalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_019cf6a1-b0fa-7faf-a736-e46a7ccbe684_totalLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Current</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime_019bdcae-e260-74a4-95f2-fa2c613053d9_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average rate during the year</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Weighted Average Interest Rate, over Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime" xlink:to="lab_us-gaap_ShortTermDebtWeightedAverageInterestRateOverTime" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019bdcae-e2e9-70c5-a8ef-7211bd396607_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfBankingOffices_019bdcae-e2e9-7e60-a252-848d6228ed85_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfBankingOffices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of banking offices</link:label>
    <link:label id="lab_fgbi_NumberOfBankingOffices_label_en-US" xlink:label="lab_fgbi_NumberOfBankingOffices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Banking Offices</link:label>
    <link:label id="lab_fgbi_NumberOfBankingOffices_documentation_en-US" xlink:label="lab_fgbi_NumberOfBankingOffices" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Banking Offices</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfBankingOffices" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfBankingOffices"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfBankingOffices" xlink:to="lab_fgbi_NumberOfBankingOffices" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan_019bdcae-e1a3-7ec8-bdd6-0ba5ea098365_terseLabel_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Past due period after which evaluation is made for discontinuation of interest accrual on loan</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan_label_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period Past Due after Which Evaluation is Made for Discontinuation of Interest Accrual on Loan</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan_documentation_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to the period past due of a loan, after which evaluation is made for discontinuation of interest accrual on a loan when management believes, after considering economic and business conditions and collection efforts, the borrower's financial condition is such that reasonable doubt exists as to the full and timely collection of principal and interest, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:href="fgbi-20251231.xsd#fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:to="lab_fgbi_PeriodPastDueAfterWhichEvaluationIsMadeForDiscontinuationOfInterestAccrualOnLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_019bdcae-e2e9-7062-a2bd-5ea1572e02c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_019bdcae-e2e9-7193-9f09-af6622238d00_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_019cf6b9-21ea-7a3d-a44e-3d38f0a5be87_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract"/>
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    <link:label id="lab_us-gaap_DividendsCommonStockCash_019bdcae-e2e9-7111-869f-58f715046196_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends on common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019bdcae-e1a3-797f-a0f8-c3e3e940b3f8_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019bdcae-e1a3-73ac-99ca-5452ed565974_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019bdcae-e1a3-715b-9642-76b42fa4df4c_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019bdcae-e1a3-73ee-b082-fd76e5f85540_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_WacoTexasMember_019d2ad6-1d5a-7dc7-b7a8-ba3c25f6e9a1_terseLabel_en-US" xlink:label="lab_fgbi_WacoTexasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Waco, Texas</link:label>
    <link:label id="lab_fgbi_WacoTexasMember_label_en-US" xlink:label="lab_fgbi_WacoTexasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Waco, Texas [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fgbi_WacoTexasMember" xlink:href="fgbi-20251231.xsd#fgbi_WacoTexasMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_WacoTexasMember" xlink:to="lab_fgbi_WacoTexasMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_019bdcae-e261-7ace-aa4a-97e1db8c0d57_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019bdcae-e261-7bff-bcf1-f06ff5786a7c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
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    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_019bdcae-e260-746f-b252-8f8b954de845_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Premises and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019bdcae-e2e9-769b-9e0b-2199a8978b71_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized_019bdcae-e2e9-79ec-8212-1a7b89d1695e_verboseLabel_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Equity Tier One Risk-Based Capital to Risk-Weighted Assets Required to Be Well Capitalized</link:label>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized_documentation_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Common Equity Tier 1 Capital ratio (Common Equity Tier 1 Capital divided by Risk-based Assets) required to be categorized as "well capitalized" under the regulatory framework for prompt corrective action.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:href="fgbi-20251231.xsd#fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:to="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredToBeWellCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019bdcae-e2e9-7ee3-8ecd-c1f79f266f2e_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019bdcae-e2e9-7dc0-83c1-d523805947d2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock issued (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_019bdcae-e1a3-7b1e-ba9b-a1a3bd18af28_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock_019bdcae-e260-7577-b3cb-8e5ab21ab934_terseLabel_en-US" xlink:label="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Notional Amounts of Financial Instruments with Off-Balance Sheet Risk</link:label>
    <link:label id="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock_label_en-US" xlink:label="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Notional Amounts of Financial Instruments with Off-Balance Sheet Risk [Table Text Block]</link:label>
    <link:label id="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock_documentation_en-US" xlink:label="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of the notional amounts of outstanding financial instruments with off-balance sheet risk.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:to="lab_fgbi_ScheduleOfNotionalAmountsOfFinancialInstrumentsWithOffBalanceSheetRiskTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized_019bdcae-e2e9-74e4-b487-f396c5da0d1f_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized"/>
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    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs_019bdcae-e1a3-77f8-a18c-8976c42f303d_terseLabel_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of charge-offs</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs_label_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity, Number Of Charge-Offs</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity, Number Of Charge-Offs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:href="fgbi-20251231.xsd#fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:to="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfChargeOffs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019bdcae-e2e9-799a-b4cf-7d810ce5a85c_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized_019bdcae-e2e9-7107-9e6b-51f8365edce3_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Common Equity Tier 1 Risk-Based Capital, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized" xlink:to="lab_us-gaap_CommonEquityTierOneCapitalRequiredToBeWellCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_019bdcae-e2e9-7fb0-8843-5e4776a966a4_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and due from banks</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019bdcae-e1a3-7451-8981-44e086ed2457_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NonInterestExpenseOther_019bdcae-e1a3-7a7b-8669-0463b5f646c3_terseLabel_en-US" xlink:label="lab_fgbi_NonInterestExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fgbi_NonInterestExpenseOther_label_en-US" xlink:label="lab_fgbi_NonInterestExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non interest Expense Other</link:label>
    <link:label id="lab_fgbi_NonInterestExpenseOther_documentation_en-US" xlink:label="lab_fgbi_NonInterestExpenseOther" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to other noninterest expenses that are not separately presented in any other noninterest expense category.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NonInterestExpenseOther" xlink:href="fgbi-20251231.xsd#fgbi_NonInterestExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NonInterestExpenseOther" xlink:to="lab_fgbi_NonInterestExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e260-7a94-86d8-cdb9b8048bff_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019bdcae-e261-7616-977e-0427c6d42ed5_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_019bdcae-e261-7a3f-b6c7-352ccb0437fa_terseLabel_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premises transferred to other real estate owned</link:label>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferToOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferToOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferToOtherRealEstate" xlink:to="lab_us-gaap_TransferToOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_019bdcae-e2e9-7820-97fe-c1b8448e12cd_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization period</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued_019bdcae-e261-7a44-a9c4-b9fdc4013887_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest on income taxes accrued</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits, Interest on Income Taxes Accrued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued" xlink:to="lab_us-gaap_UnrecognizedTaxBenefitsInterestOnIncomeTaxesAccrued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019bdcae-e2e9-7135-a63f-458494d461e9_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_019bdcae-e260-7d48-862f-c07cc0158713_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_019bdcae-e2e9-7693-a2fb-99edfba10f3d_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 10 years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleAndLeasebackTransactionGainLossNet_019bdcae-e2e9-7da7-b270-10d5a57f8e07_terseLabel_en-US" xlink:label="lab_us-gaap_SaleAndLeasebackTransactionGainLossNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale-leaseback transaction</link:label>
    <link:label id="lab_us-gaap_SaleAndLeasebackTransactionGainLossNet_label_en-US" xlink:label="lab_us-gaap_SaleAndLeasebackTransactionGainLossNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale and Leaseback Transaction, Gain (Loss), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleAndLeasebackTransactionGainLossNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleAndLeasebackTransactionGainLossNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleAndLeasebackTransactionGainLossNet" xlink:to="lab_us-gaap_SaleAndLeasebackTransactionGainLossNet" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings_019bdcae-e1a3-720a-b49b-68847c3bed53_terseLabel_en-US" xlink:label="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of interest used secured pledge borrowings</link:label>
    <link:label id="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings_label_en-US" xlink:label="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage Of Interest Used Secured Pledge Borrowings</link:label>
    <link:label id="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings_documentation_en-US" xlink:label="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The percentage of the Company's interest in a subsidiary used as a secured pledge on a borrowing.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:href="fgbi-20251231.xsd#fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:to="lab_fgbi_PercentageOfInterestUsedSecuredPledgeBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized_019bdcae-e1a3-7221-8ef9-7f89ae4b4bca_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized" xlink:to="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019bdcae-e2e9-7072-9e92-b4c4fb2d198a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_019bdcae-e2e9-7786-a08d-a72cd75f1f63_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Concentrations of Credit and Other Risks</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:to="lab_us-gaap_ConcentrationRiskDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_019bdcae-e1a3-79d5-be11-1b39d3c1becc_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum month-end outstanding</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Maximum Month-end Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:to="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock_019bdcae-e1a3-7e12-9f0d-8cf8aa46bad7_terseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Off-balance sheet financial instruments</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet Credit Exposure, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock" xlink:to="lab_us-gaap_OffBalanceSheetCreditExposurePolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard_019bdcae-e261-704d-bd55-671e97ac1b7c_terseLabel_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period past due after which loans are considered substandard</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard_label_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period Past Due after Which Loans Are Considered Substandard</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard_documentation_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period past due after which loans are considered substandard, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:href="fgbi-20251231.xsd#fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:to="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredSubstandard" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_019bdcae-e2e9-792c-9be8-9fc0c21e33fe_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember_019bdcae-e2e9-7afb-94c4-61720504bbc7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Interest Rate Period</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeDepositsWithFinancialInstitutions_019bdcae-e261-79b8-8984-571180dd4241_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeDepositsWithFinancialInstitutions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits with other banks</link:label>
    <link:label id="lab_us-gaap_InterestIncomeDepositsWithFinancialInstitutions_label_en-US" xlink:label="lab_us-gaap_InterestIncomeDepositsWithFinancialInstitutions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Deposits with Financial Institutions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeDepositsWithFinancialInstitutions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeDepositsWithFinancialInstitutions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeDepositsWithFinancialInstitutions" xlink:to="lab_us-gaap_InterestIncomeDepositsWithFinancialInstitutions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019bdcae-e1a3-7ece-a19a-93f7a70cdc22_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">(Loss) Income Before Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019bdcae-e2e9-7a75-9835-fc452490995f_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalToAverageAssets_019bdcae-e1a3-7ed4-823b-e727e13175ec_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalToAverageAssets_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalToAverageAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:to="lab_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract_019bdcae-e1a3-70c9-a0ce-4b399af263dc_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, Series A - $1,000 par value - 100,000 shares authorized</link:label>
    <link:label id="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number of Shares, Par Value and Other Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:to="lab_us-gaap_CommonStockNumberOfSharesParValueAndOtherDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019bdcae-e261-7639-a809-5eee30b9487e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_019bdcae-e2e9-7794-b052-c363dbfa2e91_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of premises and equipment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_019bdcae-e260-7cbd-9b7b-e570c20a8b38_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_label_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesByNatureOfContingencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:to="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FederalReserveRequiredCashDeposit_019bdcae-e1a3-7c38-b4b0-51e1d814f552_terseLabel_en-US" xlink:label="lab_fgbi_FederalReserveRequiredCashDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve maintained at Federal Reserve Bank</link:label>
    <link:label id="lab_fgbi_FederalReserveRequiredCashDeposit_label_en-US" xlink:label="lab_fgbi_FederalReserveRequiredCashDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Reserve Required Cash Deposit</link:label>
    <link:label id="lab_fgbi_FederalReserveRequiredCashDeposit_documentation_en-US" xlink:label="lab_fgbi_FederalReserveRequiredCashDeposit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of cash reserves required to be deposited with federal reserve bank.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FederalReserveRequiredCashDeposit" xlink:href="fgbi-20251231.xsd#fgbi_FederalReserveRequiredCashDeposit"/>
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    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019bdcae-e261-738f-ba7e-357183c45372_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019cf6a3-29b9-7d0d-8dc3-0c8d6a44d295_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Taxes Paid, Net of Refunds</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross_019bdcae-e261-782f-8744-364e8c5aa6de_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses on available for sale securities</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Debt Securities, Available-for-Sale, Unrealized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:to="lab_us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermBorrowingsAbstract_019bdcae-e2e9-72a9-baa5-494ecbbb7aec_verboseLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Short-term borrowings [Abstract]</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowingsAbstract_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermBorrowingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:to="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019bdcae-e2e9-7278-896b-7cff6144f2ae_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019bdcae-e2e9-79b6-8655-ad58ee38afe5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOperating" xlink:to="lab_us-gaap_InterestExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount_019bdcae-e2e9-709d-957d-d9b479c4a45b_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LetterOfCreditMember_019bdcae-e261-76f9-976a-6d1d9f270fac_terseLabel_en-US" xlink:label="lab_us-gaap_LetterOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and Standby letters of credit</link:label>
    <link:label id="lab_us-gaap_LetterOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LetterOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letter of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LetterOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LetterOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LetterOfCreditMember" xlink:to="lab_us-gaap_LetterOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_019bdcae-e2e9-7c14-aa9e-d101732d3efd_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average daily outstanding</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Average Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShorttermDebtAverageOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:to="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract_019bdcae-e260-71b1-9a1f-ee24d6dad6b9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total gains or losses (realized/unrealized):</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_019d2ad7-f01a-71e5-80b5-bff34229bf2a_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing_019bdcae-e261-7d3c-b078-2ac509656f48_terseLabel_en-US" xlink:label="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum extension period of short term borrowing</link:label>
    <link:label id="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing_label_en-US" xlink:label="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum Extension Period of Short Term Borrowing</link:label>
    <link:label id="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing_documentation_en-US" xlink:label="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to maximum extension period of short term borrowings of the entity, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:href="fgbi-20251231.xsd#fgbi_MaximumExtensionPeriodOfShortTermBorrowing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:to="lab_fgbi_MaximumExtensionPeriodOfShortTermBorrowing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1_019bdcae-e2e9-7bdb-b137-488ea68acd5a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance Individually Evaluated</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Individually Evaluated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019bdcae-e260-7d91-aa05-c0a155bfc838_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TravelAndEntertainmentExpense_019bdcae-e2e9-7bb8-8227-08df48c699a3_terseLabel_en-US" xlink:label="lab_us-gaap_TravelAndEntertainmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Travel and lodging</link:label>
    <link:label id="lab_us-gaap_TravelAndEntertainmentExpense_label_en-US" xlink:label="lab_us-gaap_TravelAndEntertainmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Travel and Entertainment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TravelAndEntertainmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TravelAndEntertainmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TravelAndEntertainmentExpense" xlink:to="lab_us-gaap_TravelAndEntertainmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_019bdcae-e260-70ab-9d24-2c0e1ccda93d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_019bdcae-e260-7812-9fc2-0fcbad0af1ec_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_019cf685-9926-73d5-816d-b56a37eec1d9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ParentCompanyMember_019bdcae-e261-7334-8ffb-f4194b699474_terseLabel_en-US" xlink:label="lab_srt_ParentCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Parent Company</link:label>
    <link:label id="lab_srt_ParentCompanyMember_label_en-US" xlink:label="lab_srt_ParentCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent Company [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ParentCompanyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ParentCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ParentCompanyMember" xlink:to="lab_srt_ParentCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome_019bdcae-e261-7a76-8295-c6551439f734_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of category</link:label>
    <link:label id="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome_label_en-US" xlink:label="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Ratio of Individual Loans Receivable to All Loans Before Unearned Income</link:label>
    <link:label id="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The individual loans receivable as a percentage of the carrying amount of all loans before unearned income.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:to="lab_fgbi_FinancingReceivableRatioOfIndividualLoansReceivableToAllLoansBeforeUnearnedIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy_019bdcae-e261-7fc3-a499-cc7088a684d0_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers of Financial Assets</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing of Financial Assets, Transfers of Financial Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTransfersOfFinancialAssetsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019bdcae-e2e9-7703-adbc-3c0649906423_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019bdcae-e261-72e2-ac17-937261ada97d_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019bdcae-e2e9-7471-9d24-48ea19924761_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_019bdcae-e261-75ad-b4e4-69163dea4bef_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on debt</link:label>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseLongTermDebt" xlink:to="lab_us-gaap_InterestExpenseLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019bdcae-e2e9-70ee-8980-07bd2dcb0782_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_019bdcae-e260-703e-99b5-e043ac9c3b5b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_019bdcae-e260-7b54-9516-5aabb94cbc64_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease)in federal funds purchased and short-term borrowings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_019bdcae-e260-7c39-87ad-c103d8312e73_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in short-term borrowings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Repayments of) Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRepaymentsOfShortTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:to="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019bdcae-e261-795e-b83a-8285cb7a3ff7_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019bdcae-e260-776e-abdf-e6a16a51327b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRatio_019bdcae-e2e9-7a3f-8cf7-f733daf2fb5a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRatio_label_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Common Equity Tier 1 Risk-Based Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonEquityTierOneCapitalRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonEquityTierOneCapitalRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonEquityTierOneCapitalRatio" xlink:to="lab_us-gaap_CommonEquityTierOneCapitalRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_InvestmentsInSubsidiaries_019bdcae-e261-798f-92c8-e29fb0e944be_terseLabel_en-US" xlink:label="lab_fgbi_InvestmentsInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment in bank subsidiary</link:label>
    <link:label id="lab_fgbi_InvestmentsInSubsidiaries_label_en-US" xlink:label="lab_fgbi_InvestmentsInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments In Subsidiaries</link:label>
    <link:label id="lab_fgbi_InvestmentsInSubsidiaries_documentation_en-US" xlink:label="lab_fgbi_InvestmentsInSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">A company's investment in its wholly-owned subsidiaries as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_InvestmentsInSubsidiaries" xlink:href="fgbi-20251231.xsd#fgbi_InvestmentsInSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_InvestmentsInSubsidiaries" xlink:to="lab_fgbi_InvestmentsInSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_019bdcae-e261-757e-81b2-f96974b4a121_negatedLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less Than 12 Months, Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock_019bdcae-e1a3-791e-91ec-9c3db90d4feb_verboseLabel_en-US" xlink:label="lab_us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Condensed Parent Company Information</link:label>
    <link:label id="lab_us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Financial Information of Parent Company Only Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CondensedFinancialInformationOfParentCompanyOnlyDisclosureTextBlock"/>
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    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_019bdcae-e261-7be9-9dab-abab65527d5e_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded lending commitments</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnfundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019bdcae-e260-756b-86f8-35eb8f4e8125_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_019bdcae-e261-7e77-8cf8-9e15d34f2143_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-lived intangible assets</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill"/>
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    <link:label id="lab_us-gaap_InterestExpenseTimeDeposits_019bdcae-e1a3-7fa5-b193-849c738a0794_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseTimeDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time deposits</link:label>
    <link:label id="lab_us-gaap_InterestExpenseTimeDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseTimeDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Time Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseTimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseTimeDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseTimeDeposits" xlink:to="lab_us-gaap_InterestExpenseTimeDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_019bdcae-e2e9-7dd5-a091-d35d74dcaa47_totalLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Provision</link:label>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_label_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, And Off-Balance Sheet, Credit Loss, Liability, Credit Loss Expense (Reversal)</link:label>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, And Off-Balance Sheet, Credit Loss, Liability, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:to="lab_fgbi_FinancingReceivableExcludingAccruedInterestAndOffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncome_019bdcae-e261-7cf4-8cf0-f37e5b0e18f9_totalLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Noninterest Income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncome" xlink:to="lab_us-gaap_NoninterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019bdcae-e2e9-7645-a7a3-4d0d00003fef_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract_019bdcae-e2e9-7a3e-90de-cedc4336c8cf_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of allowance and loans individually and collectively evaluated for impairment [Abstract]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Additional Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossAdditionalInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_019bdcae-e261-79a8-92a8-94ca5425ec47_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gains on sale of loans</link:label>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_label_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sales of Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSalesOfLoansNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:to="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_019bdcae-e261-79a5-8606-8c96c4267ca6_negatedLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accumulated Unrecognized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
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    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_019bdcae-e260-7757-8333-68404f7ccac1_verboseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_019bdcae-e261-75ae-a9c2-280fd5f1c0a5_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noninterest Expense:</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpenseAbstract" xlink:to="lab_us-gaap_NoninterestExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndDueFromBanks_019bdcae-e260-704e-93f7-f1c3d5a084d7_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndDueFromBanks" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and due from banks</link:label>
    <link:label id="lab_us-gaap_CashAndDueFromBanks_label_en-US" xlink:label="lab_us-gaap_CashAndDueFromBanks" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Due from Banks</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndDueFromBanks" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndDueFromBanks"/>
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    <link:label id="lab_us-gaap_LegalFees_019bdcae-e261-7c7e-a75f-bfbbe7170af8_terseLabel_en-US" xlink:label="lab_us-gaap_LegalFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal and professional fees</link:label>
    <link:label id="lab_us-gaap_LegalFees_label_en-US" xlink:label="lab_us-gaap_LegalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LegalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LegalFees"/>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_019bdcae-e2e9-73a8-ade1-ec7a421a1961_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
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    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne_019bdcae-e2e9-79e4-8269-42011a2a5492_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial fixed rate period, tranche one</link:label>
    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne_label_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Initial Fixed Rate Period, Tranche One</link:label>
    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Initial Fixed Rate Period, Tranche One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableInitialFixedRatePeriodTrancheOne"/>
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    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_019cf6a0-78a1-783d-9802-79eef274a810_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current:</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing_019bdcae-e261-7d59-b2a9-7ca667c4eb52_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recorded Investment 90 Days Accruing</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, 90 Days or More Past Due, Still Accruing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterest90DaysOrMorePastDueStillAccruing" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019bdcae-e2e9-7f0d-99a2-20d958009be8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Amortization Expense of Core Deposit Intangible Assets for Next Five Years</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019bdcae-e1a3-748f-aac5-114d7c543d29_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019bdcae-e2e9-7e87-853d-c35ab5b165df_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019bdcae-e261-78cd-b1bf-d4984ec12e8d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_019bdcae-e261-717c-baa8-ee8ad10437c7_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities (including FHLB stock)</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Securities, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:to="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019bdcae-e261-76b8-9681-9de98f4e42cc_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Benefit) Provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019bdcae-e261-7b09-a021-e34ad3999d3f_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019bdcae-e261-7626-a61b-d93666f9657a_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019bdcae-e1a3-726e-a6e1-0b3c3ea454b5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, basis spread on variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019bdcae-e1a3-7f31-98f6-e76ee5a32e30_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FederalFundsSoldFairValueDisclosure_019bdcae-e1a3-7d1d-a499-566850eb9670_terseLabel_en-US" xlink:label="lab_fgbi_FederalFundsSoldFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal funds sold</link:label>
    <link:label id="lab_fgbi_FederalFundsSoldFairValueDisclosure_label_en-US" xlink:label="lab_fgbi_FederalFundsSoldFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Funds Sold, Fair Value Disclosure</link:label>
    <link:label id="lab_fgbi_FederalFundsSoldFairValueDisclosure_documentation_en-US" xlink:label="lab_fgbi_FederalFundsSoldFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Funds Sold, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FederalFundsSoldFairValueDisclosure" xlink:href="fgbi-20251231.xsd#fgbi_FederalFundsSoldFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FederalFundsSoldFairValueDisclosure" xlink:to="lab_fgbi_FederalFundsSoldFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019bdcae-e2e9-742a-b53e-cd6b7debb090_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of year</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019bdcae-e2e9-7c59-8122-ab8a343071ab_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance as of end of year</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019bdcae-e2e9-74f0-a204-0d6c6229375e_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember_019bdcae-e2e9-759b-8c9c-9d6d9c55f6e5_verboseLabel_en-US" xlink:label="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unfunded Commitments under lines of credit</link:label>
    <link:label id="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember_label_en-US" xlink:label="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Commitment Under Lines of Credit [Member]</link:label>
    <link:label id="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember_documentation_en-US" xlink:label="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The aggregate unused portion of a line of credit that is available to the borrower to withdrawn upon.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:href="fgbi-20251231.xsd#fgbi_UnfundedCommitmentUnderLinesOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:to="lab_fgbi_UnfundedCommitmentUnderLinesOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesAfterYearFive_019d3ffa-4963-7f9f-86f7-11f9cf7ea9b3_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesAfterYearFive_label_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposit Maturities, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositMaturitiesAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDepositMaturitiesAfterYearFive" xlink:to="lab_us-gaap_TimeDepositMaturitiesAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_019bdcae-e2e9-7d52-8085-33184a8ff826_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
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    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019bdcae-e2e9-73d9-a703-cec5faba7cca_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_019bdcae-e2e9-77e0-b8d5-328e7efcea85_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired value</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Gross</link:label>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_019bdcae-e260-7752-9865-03f63c316839_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
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    <link:label id="lab_us-gaap_BankingRegulationCapitalConservationBufferTotalRiskBasedCapitalActual_019bdcae-e2e9-7cf9-ac3f-ef85bf96673e_terseLabel_en-US" xlink:label="lab_us-gaap_BankingRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital conservation buffer</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BankingRegulationCapitalConservationBufferTotalRiskBasedCapitalActual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankingRegulationCapitalConservationBufferTotalRiskBasedCapitalActual"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_019bdcae-e261-7e8c-b6ed-ebc1f0aed460_verboseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contributions to savings plan</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Employer Discretionary Contribution Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount"/>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_019c7b9f-9d36-71d9-a14f-9497ad97c275_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in right of use asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalAbstract_019bdcae-e261-7eda-a88d-c31b2e0ab98d_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 Capital, Amount</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalAbstract"/>
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    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_019bdcae-e2e9-7a37-ad66-5692fa8e4716_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and Building Improvements</link:label>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_label_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building and Building Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingAndBuildingImprovementsMember"/>
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    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_019cf6a8-98e0-702d-b89e-7a9302c8f7a7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, Federal, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidFederalAfterRefundReceived"/>
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    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
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    <link:label id="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsLineItems_019bdcae-e2e9-74a5-a9b2-736ffbdbb749_terseLabel_en-US" xlink:label="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compliance with Regulatory Capital Requirements under Banking Regulations [Line Items]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome_019cf6ae-2f41-7d0d-8ad6-ce36d5e70adb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax exempt municipal income</link:label>
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    <link:label id="lab_us-gaap_NoninterestIncomeOtherOperatingIncome_019bdcae-e261-7545-a7d2-0fbd741e8589_verboseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits_019d308d-6ea8-713a-b988-651b99cb2f9f_terseLabel_en-US" xlink:label="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal group, deposits</link:label>
    <link:label id="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits_label_en-US" xlink:label="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Deposits</link:label>
    <link:label id="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits_documentation_en-US" xlink:label="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:href="fgbi-20251231.xsd#fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:to="lab_fgbi_DisposalGroupIncludingDiscontinuedOperationDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock_019bdcae-e1a3-7ea7-86d6-488b5172eed2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fixed and Floating Rate Loans by Contractual Maturity, Excluding Nonaccrual Loans</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivables, Minimum Payments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesMinimumPaymentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019bdcae-e1a3-7916-89c3-1067c4c6f030_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Cash (Used In) Provided by Operating Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019bdcae-e261-71ac-833d-1f2f8900fad1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability_019bdcae-e2e9-7a99-b859-08571b6c9bf4_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional value</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure, off-Balance-Sheet Risks, Face Amount, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability" xlink:to="lab_us-gaap_FairValueDisclosureOffbalanceSheetRisksFaceAmountLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned_019cf6cb-4f5c-73cc-bfd7-b0b3b0264298_negatedTerseLabel_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other real estate owned</link:label>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned_label_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other Real Estate Owned</link:label>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned_documentation_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount before allocation of valuation allowances of deferred tax Liabilities attributable to other real estate owned.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:href="fgbi-20251231.xsd#fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:to="lab_fgbi_DeferredTaxLiabilitiesOtherRealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019bdcae-e2e9-74e7-bfe9-1e9a27d923ae_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for sale, at fair value (cost of $674,139 and $284,321, respectively)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019bdcae-e2e9-7df4-a67c-05cc40b74d6b_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019bdcae-e2e9-7ff5-9500-50098a535c69_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total available for sale securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019bdcae-e2e9-76b1-b39b-3135a6fa3f69_netLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Securities available for sale measured at fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_019bdcae-e261-7183-badb-a59e1d3ec5e1_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of other real estate owned</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:to="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_019bdcae-e2e9-7f32-b654-28defd08f00f_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated useful life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019bdcae-e2e9-7589-9166-d0ffff630a34_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_019bdcae-e2e9-74db-b84a-41a67cf93de0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateLineItems_019bdcae-e261-7474-bbbb-2af575bc2baa_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:label id="lab_us-gaap_RealEstateLineItems_label_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLineItems" xlink:to="lab_us-gaap_RealEstateLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_019bdcae-e260-72c8-9dc9-ef7464a66629_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Interest Income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapital_019bdcae-e2e9-74dc-808b-4bd6d47020f6_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapital_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneRiskBasedCapital" xlink:to="lab_us-gaap_TierOneRiskBasedCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019bdcae-e2e9-7cd5-85e0-43993122c220_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_019bdcae-e2e9-753b-8162-4de9b24cf411_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CommercialLeasesMember_019bdcae-e2e9-7c45-9371-79b1a183a63b_terseLabel_en-US" xlink:label="lab_fgbi_CommercialLeasesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial leases</link:label>
    <link:label id="lab_fgbi_CommercialLeasesMember_label_en-US" xlink:label="lab_fgbi_CommercialLeasesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Leases [Member]</link:label>
    <link:label id="lab_fgbi_CommercialLeasesMember_documentation_en-US" xlink:label="lab_fgbi_CommercialLeasesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CommercialLeasesMember" xlink:href="fgbi-20251231.xsd#fgbi_CommercialLeasesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CommercialLeasesMember" xlink:to="lab_fgbi_CommercialLeasesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019bdcae-e1a3-7db1-9ace-2a34282357f6_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityRestrictions_019bdcae-e1a3-7721-abbf-c2b2676c98b5_terseLabel_en-US" xlink:label="lab_us-gaap_EquityRestrictions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity restrictions</link:label>
    <link:label id="lab_us-gaap_EquityRestrictions_label_en-US" xlink:label="lab_us-gaap_EquityRestrictions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Restrictions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityRestrictions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityRestrictions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityRestrictions" xlink:to="lab_us-gaap_EquityRestrictions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_019bdcae-e2e9-77cf-b9e2-751911ed7bd6_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_019bdcae-e261-7567-9f0e-1ec87a412125_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated, year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019cb291-e554-787f-a70c-9acef2380cd5_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019bdcae-e261-7f57-b189-e0c530cf53e4_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubstandardMember_019bdcae-e261-7ca1-b56e-af1f295fd51d_terseLabel_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Substandard</link:label>
    <link:label id="lab_us-gaap_SubstandardMember_label_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Substandard [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubstandardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubstandardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubstandardMember" xlink:to="lab_us-gaap_SubstandardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_019bdcae-e2e9-7de9-bef4-50bdbed836b0_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Interest Income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SpecialMentionMember_019bdcae-e261-78f2-b646-a94187e6093a_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special Mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019bdcae-e2e9-7a4e-9c96-862b466825e5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_019bdcae-e2e9-7261-8164-00f906b12d66_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans, net</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_RegulatoryAssessment_019bdcae-e260-7432-b18e-a5fd5ad2fa54_terseLabel_en-US" xlink:label="lab_fgbi_RegulatoryAssessment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Regulatory assessment</link:label>
    <link:label id="lab_fgbi_RegulatoryAssessment_label_en-US" xlink:label="lab_fgbi_RegulatoryAssessment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory assessment</link:label>
    <link:label id="lab_fgbi_RegulatoryAssessment_documentation_en-US" xlink:label="lab_fgbi_RegulatoryAssessment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to non interest expense incurred for regulatory assessment during the period by the entity.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_RegulatoryAssessment" xlink:href="fgbi-20251231.xsd#fgbi_RegulatoryAssessment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_RegulatoryAssessment" xlink:to="lab_fgbi_RegulatoryAssessment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_019bdcae-e2e9-763e-a2f1-db561d8fb332_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_019bdcae-e261-7f4d-9691-f127486dba3d_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_019bdcae-e261-78b4-844b-2e3f39e48e5d_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed Securities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy_019bdcae-e1a3-7253-b81e-d3801fc17fcf_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy"/>
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    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_019bdcae-e1a3-7a1f-9f7d-ea6fdc7af1cc_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Repayment of long-term borrowings</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_019bdcae-e1a3-7d10-9ca4-956396e38530_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayment of long-term debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019bdcae-e2e9-7b55-922b-e5548bd1b592_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract_019bdcae-e2e9-77e5-8ace-d8fa6903c51e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current period gross charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff, by Origination Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyNatureDomain_019bdcae-e1a3-7449-965c-0c793bf2475e_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyNatureDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency, Nature [Domain]</link:label>
    <link:label id="lab_us-gaap_LossContingencyNatureDomain_label_en-US" xlink:label="lab_us-gaap_LossContingencyNatureDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Nature [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyNatureDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyNatureDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyNatureDomain" xlink:to="lab_us-gaap_LossContingencyNatureDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DirectorsAndExecutiveOfficersMember_019bdcae-e2e9-7cf7-9cec-8780402f2a2e_terseLabel_en-US" xlink:label="lab_fgbi_DirectorsAndExecutiveOfficersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Directors and Executive Officers</link:label>
    <link:label id="lab_fgbi_DirectorsAndExecutiveOfficersMember_label_en-US" xlink:label="lab_fgbi_DirectorsAndExecutiveOfficersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Directors and Executive Officers [Member]</link:label>
    <link:label id="lab_fgbi_DirectorsAndExecutiveOfficersMember_documentation_en-US" xlink:label="lab_fgbi_DirectorsAndExecutiveOfficersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Person serving on the board of directors (who collectively have responsibility for governing the entity). One of the ranking officers of the entity, appointed to the position by the board of directors.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DirectorsAndExecutiveOfficersMember" xlink:href="fgbi-20251231.xsd#fgbi_DirectorsAndExecutiveOfficersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DirectorsAndExecutiveOfficersMember" xlink:to="lab_fgbi_DirectorsAndExecutiveOfficersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure_019bdcae-e261-7426-87f1-9b5991228e3c_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableModificationsLineItems_019bdcae-e261-731a-b80b-347dd4c61b91_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Troubled Debt Restructuring [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableModificationsLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Modified [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableModificationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableModificationsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableModificationsLineItems" xlink:to="lab_us-gaap_FinancingReceivableModificationsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_019bdcae-e261-781b-a360-b15a38137621_negatedLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Repossessed asset write downs, gains and losses on dispositions</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gains (Losses) on Sales of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnSalesOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:to="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_019bdcae-e261-7dca-a7ac-389c7c3b32f4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList"/>
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    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_019bdcae-e2e9-751b-838f-369c40f2adb9_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income:</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestExpense_019bdcae-e261-7e4e-ad3e-d08ee77469a3_totalLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Noninterest Expense</link:label>
    <link:label id="lab_us-gaap_NoninterestExpense_label_en-US" xlink:label="lab_us-gaap_NoninterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpense" xlink:to="lab_us-gaap_NoninterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_019bdcae-e261-7039-894a-a67c04e35a47_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Periodic principal payment</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Periodic Payment, Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_019bdcae-e1a3-79bc-a0fa-236a62c6694f_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Remaining Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecurities_019bdcae-e2e9-7943-98a9-58734e9efefe_totalLabel_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Investment securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecurities_019bdcae-e2e9-7144-bc21-92c4102bf879_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_MarketableSecurities_label_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecurities" xlink:to="lab_us-gaap_MarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_019bdcae-e261-74e7-9e5d-2d0968eeff7b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
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    <link:label id="lab_us-gaap_PaymentDeferralMember_019bdcae-e2e9-7d31-903a-003b2f2e549a_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment Deferral</link:label>
    <link:label id="lab_us-gaap_PaymentDeferralMember_label_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Deferral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentDeferralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentDeferralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentDeferralMember" xlink:to="lab_us-gaap_PaymentDeferralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesTextBlock_019bdcae-e2e9-7432-8737-3734c1fd9f51_verboseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses on Loans</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019bdcae-e261-7bb7-904f-dbe754ebfbb3_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_019bdcae-e261-7789-89d6-dda852f833e1_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noninterest Income:</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FeesAndCommissions1_019bdcae-e261-709e-8d3a-8e367bbfbf7d_terseLabel_en-US" xlink:label="lab_fgbi_FeesAndCommissions1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service charges, commissions and fees</link:label>
    <link:label id="lab_fgbi_FeesAndCommissions1_label_en-US" xlink:label="lab_fgbi_FeesAndCommissions1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fees And Commissions 1</link:label>
    <link:label id="lab_fgbi_FeesAndCommissions1_documentation_en-US" xlink:label="lab_fgbi_FeesAndCommissions1" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fees And Commissions 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FeesAndCommissions1" xlink:href="fgbi-20251231.xsd#fgbi_FeesAndCommissions1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FeesAndCommissions1" xlink:to="lab_fgbi_FeesAndCommissions1" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfCondensedFinancialStatementsTable_019bdcae-e261-7061-8620-3562e126bcf3_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Condensed Financial Statements [Table]</link:label>
    <link:label id="lab_srt_ScheduleOfCondensedFinancialStatementsTable_label_en-US" xlink:label="lab_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Financial Statements [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfCondensedFinancialStatementsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:to="lab_srt_ScheduleOfCondensedFinancialStatementsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019bdcae-e261-7606-beb2-7ed445da5a93_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019cf7a0-4cde-753a-b2a4-94060c2968c0_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating income</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_019bdcae-e1a3-7a7e-a7bf-c1b113ed65d6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Obligations on Long-term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfBranchesSold_019d2ad6-1d5a-7b5e-b47d-b7defb34289f_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfBranchesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of branches sold</link:label>
    <link:label id="lab_fgbi_NumberOfBranchesSold_label_en-US" xlink:label="lab_fgbi_NumberOfBranchesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Branches Sold</link:label>
    <link:label id="lab_fgbi_NumberOfBranchesSold_documentation_en-US" xlink:label="lab_fgbi_NumberOfBranchesSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Branches Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfBranchesSold" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfBranchesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfBranchesSold" xlink:to="lab_fgbi_NumberOfBranchesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019bdcae-e2e9-7c02-ac28-a84b27c30613_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates_019bdcae-e2e9-792e-b88c-bbf7649c3d73_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds invested in bank subsidiary</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Interest in Subsidiaries and Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:to="lab_us-gaap_PaymentsToAcquireInterestInSubsidiariesAndAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019bdcae-e260-7b0b-bf14-f0ef59fa4a0b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Credit Exposure of Loan Portfolio, Including Loans Acquired with Deteriorated Credit Quality, by Specific Credit Ratings</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure_019bdcae-e260-78f6-ae06-4dad0a9eb940_verboseLabel_en-US" xlink:label="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Individually evaluated loans measured at fair value</link:label>
    <link:label id="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impaired Loans Receivable Fair Value Disclosure</link:label>
    <link:label id="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure_documentation_en-US" xlink:label="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the portion of the balance sheet assertion valued at fair value by the entity whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission. This element represents the fair value of impaired loans as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:href="fgbi-20251231.xsd#fgbi_ImpairedLoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:to="lab_fgbi_ImpairedLoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent_019bdcae-e261-7294-9f64-0a33fc0e3510_totalLabel_en-US" xlink:label="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">(Loss) income before (decrease) increase in equity in undistributed earnings of subsidiary</link:label>
    <link:label id="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent_label_en-US" xlink:label="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Loss From Continuing Operations Net Of Tax, Before Equity Method Investments, Attributable To Parent</link:label>
    <link:label id="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent_documentation_en-US" xlink:label="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Loss From Continuing Operations Net Of Tax, Before Equity Method Investments, Attributable To Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:href="fgbi-20251231.xsd#fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:to="lab_fgbi_IncomeLossFromContinuingOperationsNetOfTaxBeforeEquityMethodInvestmentsAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy_019bdcae-e261-7a71-b70a-d8c8df737d0d_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:to="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestBearingDepositLiabilities_019bdcae-e260-717e-817f-42a930ea67d7_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noninterest-bearing demand</link:label>
    <link:label id="lab_us-gaap_NoninterestBearingDepositLiabilities_label_en-US" xlink:label="lab_us-gaap_NoninterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest-Bearing Deposit Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestBearingDepositLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestBearingDepositLiabilities"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentsDisclosureTextBlock_019bdcae-e1a3-7504-92ee-1d269a6daa4e_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityTotalMember_019bdcae-e261-7079-a320-7df7b2fc6497_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityTotalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity, Total</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityTotalMember_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityTotalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity, Total [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityTotalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityTotalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityTotalMember" xlink:to="lab_us-gaap_StockholdersEquityTotalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
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    <link:label id="lab_dei_EntityFilerCategory_019bdcae-e261-7d76-b99f-969babbecf49_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
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    <link:label id="lab_us-gaap_DividendIncomeOperating_019bdcae-e261-76d6-a1f7-746d16668f88_verboseLabel_en-US" xlink:label="lab_us-gaap_DividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Dividends received from bank subsidiary</link:label>
    <link:label id="lab_us-gaap_DividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_DividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendIncomeOperating"/>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets_019bdcae-e261-747d-9be3-1d8e0b71d4fb_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital Ratio, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets"/>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_019bdcae-e261-72a8-a1cc-a6dd43fa1861_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_019bdcae-e261-747a-8183-4d605119605b_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal income taxes at statutory rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019bdcae-e261-7a1c-9d65-17310017bb83_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_019bdcae-e261-7c53-8eb0-69d55c81f711_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Other Real Estate Owned and Foreclosed Property</link:label>
    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_label_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Acquired Through Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAcquiredThroughForeclosure"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019bdcae-e261-76b6-803d-2e26ce89a897_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">December 31, 2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_019bdcae-e2e9-782d-b259-cfee84ca3f8c_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
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    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
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    <link:label id="lab_dei_EntityAddressAddressLine1_019bdcae-e261-7bc1-b447-ae59ff091c7d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy_019bdcae-e261-7a54-a992-917c4c5befc5_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Sale [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLoanAndLeaseReceivablesHeldForSalePolicy"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019bdcae-e261-71b0-9e76-5f4a745b2558_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income/(Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_019c7ac5-3879-7a99-aba1-9a7d377e3534_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock issued in subordinated debt conversion (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_019bdcae-e260-7006-a4ff-606f5b522c13_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentAxis"/>
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    <link:label id="lab_us-gaap_StockIssued1_label_en-US" xlink:label="lab_us-gaap_StockIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssued1"/>
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    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward_019bdcae-e1a3-75f3-b464-92e609b8d46a_terseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward_label_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditLossLiabilityRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward" xlink:to="lab_us-gaap_OffBalanceSheetCreditLossLiabilityRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_019bdcae-e260-75a4-8f68-c8898e2c9238_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentDomain" xlink:to="lab_us-gaap_InternalCreditAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember_019bdcae-e2e9-7da9-9d41-b790b5587bd0_terseLabel_en-US" xlink:label="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Architectural Services To Gasaway Bankston Architects</link:label>
    <link:label id="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember_label_en-US" xlink:label="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Architectural Services To Gasaway Bankston Architects [Member]</link:label>
    <link:label id="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember_documentation_en-US" xlink:label="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Architectural Services To Gasaway Bankston Architects</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:href="fgbi-20251231.xsd#fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:to="lab_fgbi_ArchitecturalServicesToGasawayBankstonArchitectsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember_019d308e-4268-7894-afab-e9bfd4123a4a_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Held-for-Sale, Not Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember_label_en-US" xlink:label="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Held-for-Sale, Not Discontinued Operations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:to="lab_us-gaap_DisposalGroupHeldforsaleNotDiscontinuedOperationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock_019bdcae-e2e9-793e-aaf7-2751deff0a0d_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Significant Components of Other Noninterest Expense</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Nonoperating Income (Expense) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfOtherNonoperatingIncomeExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_019bdcae-e261-73db-95a7-471417176ae2_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwards" xlink:to="lab_us-gaap_OperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_019bdcae-e2e9-7f17-84b7-d8454b6c041e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated, year five</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Five, Originated, Four Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivables30To89DaysPastDueMember_019bdcae-e261-7cc4-9095-226ee7da559f_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">30-89 Days Past Due</link:label>
    <link:label id="lab_fgbi_FinancingReceivables30To89DaysPastDueMember_label_en-US" xlink:label="lab_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivables 30 To 89 Days Past Due [Member]</link:label>
    <link:label id="lab_fgbi_FinancingReceivables30To89DaysPastDueMember_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing receivables that are more than 29 days past due but fewer than 90 days past due.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivables30To89DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:to="lab_fgbi_FinancingReceivables30To89DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019bdcae-e2e9-70ff-a0fa-1069b4de54d5_verboseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Salaries and employee benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019bdcae-e2e9-7851-9c60-d96e1c895f26_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Salaries &amp; Benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance_019bdcae-e260-7cb6-9d66-4ef8b42b0abf_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">With Related Allowance</link:label>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance_label_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, With Allowance</link:label>
    <link:label id="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, With Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:to="lab_fgbi_FinancingReceivableExcludingAccruedInterestNonaccrualWithAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets_019bdcae-e2e9-72ed-8172-8d374909ea04_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital Ratio, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacyToAverageAssets"/>
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    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_019bdcae-e260-763a-b926-fe6ca239c08e_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_label_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019bdcae-e261-7578-bf2b-607b328f4453_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_019bdcae-e261-7095-9867-36a428983e56_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less Than 12 Months, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets_019bdcae-e2e9-75cd-be2e-707781515747_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:to="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_019bdcae-e2e9-73b9-a5fa-d6ef15d36799_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FixedRateLoansMember_019bdcae-e2e9-7daa-a22f-145e446de22e_verboseLabel_en-US" xlink:label="lab_fgbi_FixedRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fixed</link:label>
    <link:label id="lab_fgbi_FixedRateLoansMember_label_en-US" xlink:label="lab_fgbi_FixedRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate Loans [Member]</link:label>
    <link:label id="lab_fgbi_FixedRateLoansMember_documentation_en-US" xlink:label="lab_fgbi_FixedRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the fixed rate loans.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FixedRateLoansMember" xlink:href="fgbi-20251231.xsd#fgbi_FixedRateLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FixedRateLoansMember" xlink:to="lab_fgbi_FixedRateLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_019bdcae-e1a3-758d-8d54-7db0b74cc3ea_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">12 Months or More, Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_019bdcae-e261-73a1-8958-31965b60ac02_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Nonaccrual Loans by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019bdcae-e1a3-7544-87e6-bd2f44482a6d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract_019bdcae-e2e9-79f6-8d62-f9165b56e5bb_terseLabel_en-US" xlink:label="lab_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Condensed Financial Information Disclosure [Abstract]</link:label>
    <link:label id="lab_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract_label_en-US" xlink:label="lab_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Financial Information Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract" xlink:to="lab_srt_CondensedFinancialInformationOfParentCompanyOnlyDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, All Other Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsAllOtherInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:to="lab_us-gaap_InvestmentsAllOtherInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract_019bdcae-e261-7b58-96e6-282977b69337_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements and Changes in Accounting Principles [Abstract]</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract" xlink:to="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent_019bdcae-e261-77f8-ac6b-c86edbc6f8f4_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Change in unrealized gains on securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Available-for-Sale Securities Adjustment, before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent_019bdcae-e260-7c8c-b72c-6d4ccec79309_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Tax effect</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Available-for-Sale Securities, Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DepositsTextBlock_019bdcae-e1a3-7b2d-b7a4-ba0cad083f3f_verboseLabel_en-US" xlink:label="lab_fgbi_DepositsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_fgbi_DepositsTextBlock_label_en-US" xlink:label="lab_fgbi_DepositsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits [Text Block]</link:label>
    <link:label id="lab_fgbi_DepositsTextBlock_documentation_en-US" xlink:label="lab_fgbi_DepositsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The entire disclosure of deposits.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DepositsTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_DepositsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DepositsTextBlock" xlink:to="lab_fgbi_DepositsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfEmployeesPartOfEquityPlan_019bdcae-e261-739f-833d-c0e2cb736901_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of employees part of equity plan</link:label>
    <link:label id="lab_fgbi_NumberOfEmployeesPartOfEquityPlan_label_en-US" xlink:label="lab_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Employees Part of Equity Plan</link:label>
    <link:label id="lab_fgbi_NumberOfEmployeesPartOfEquityPlan_documentation_en-US" xlink:label="lab_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Employees Part of Equity Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfEmployeesPartOfEquityPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:to="lab_fgbi_NumberOfEmployeesPartOfEquityPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy_019bdcae-e261-71a1-a152-d9a13d2387d5_terseLabel_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Equity Tier One Risk Based Capital To Risk Weighted Assets Required For Capital Adequacy</link:label>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy_documentation_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The minimum Common Equity Tier 1 Capital ratio (Common Equity Tier 1 Capital divided by Risk-based Assets) required for capital adequacy purposes under the regulatory framework for prompt corrective action.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:href="fgbi-20251231.xsd#fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:to="lab_fgbi_CommonEquityTierOneRiskBasedCapitalToRiskWeightedAssetsRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_019bdcae-e2e9-7020-9faf-2c7451c1f2fc_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of credit amount at FHLB</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019bdcae-e260-792d-a222-a2a32b1b8d9d_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_019bdcae-e2e9-712d-9ffe-74b0714e20b4_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019bdcae-e261-792b-8a36-9c58d268064f_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019bdcae-e1a3-7958-a5c8-69e9b6003ab2_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_019bdcae-e261-7c42-bd06-892acd4da731_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net decrease in loans</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:to="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingExpense_019bdcae-e261-77b6-9c60-6ef24954eabe_verboseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Advertising expense</link:label>
    <link:label id="lab_us-gaap_AdvertisingExpense_label_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingExpense" xlink:to="lab_us-gaap_AdvertisingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_019cf6a1-4945-7cbb-b286-74f0eb3029d6_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred:</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalized_019bdcae-e261-7b76-a4a7-2731113d06b0_verboseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredToBeWellCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:to="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OneToFourFamilyMember_019bdcae-e260-751c-8385-a69ec9e41667_terseLabel_en-US" xlink:label="lab_fgbi_OneToFourFamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1- 4 Family</link:label>
    <link:label id="lab_fgbi_OneToFourFamilyMember_label_en-US" xlink:label="lab_fgbi_OneToFourFamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">One to Four Family [Member]</link:label>
    <link:label id="lab_fgbi_OneToFourFamilyMember_documentation_en-US" xlink:label="lab_fgbi_OneToFourFamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the purchase of 1 to 4 family residential real property.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OneToFourFamilyMember" xlink:href="fgbi-20251231.xsd#fgbi_OneToFourFamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OneToFourFamilyMember" xlink:to="lab_fgbi_OneToFourFamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019bdcae-e1a3-7694-bd78-6527c1cf46fb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019bdcae-e1a3-7924-972f-d8ad9a704e34_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual_019bdcae-e260-7d2c-b755-de02d2c7585d_totalLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Subtotal</link:label>
    <link:label id="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual_label_en-US" xlink:label="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Gross Carrying Amount Net Nonaccrual</link:label>
    <link:label id="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans amount before allowance of loans and leases held in portfolio and those classified as nonaccrual, including but not limited to, commercial and consumer loans.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:to="lab_fgbi_FinancingReceivableGrossCarryingAmountNetNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember_019bdcae-e260-7f4e-918d-d14132b1e3a5_terseLabel_en-US" xlink:label="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Loans Except Mortgage Loans</link:label>
    <link:label id="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember_label_en-US" xlink:label="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Financing Receivables Except Mortgage Loans [Member]</link:label>
    <link:label id="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember_documentation_en-US" xlink:label="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">All financing receivables related to all financing receivables except mortgage loans.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:href="fgbi-20251231.xsd#fgbi_AllFinancingReceivablesExceptMortgageLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:to="lab_fgbi_AllFinancingReceivablesExceptMortgageLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019bdcae-e2e9-7457-aacc-4383e7690cbd_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearFour_019bdcae-e2e9-7a8f-8d68-a1df43b24e3e_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
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    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_019bdcae-e1a3-7fa5-bc54-ca72782e1979_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableDeferredIncome_019bdcae-e261-7935-9925-e3165ae56998_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableDeferredIncome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unearned income</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableDeferredIncome_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableDeferredIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Deferred Commitment Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableDeferredIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableDeferredIncome"/>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_019bdcae-e2e9-7f14-8d65-2f2db4691f4b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019bdcae-e261-71fd-b806-86611548aecb_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through 10 years</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_019bdcae-e261-71f1-aa21-648a7c761d37_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 Months or More, Number of Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019bdcae-e261-7e92-8e8b-5c842a565f66_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_srt_CondensedFinancialStatementsCaptionsLineItems_019bdcae-e261-732a-a4fa-c493157d92e6_terseLabel_en-US" xlink:label="lab_srt_CondensedFinancialStatementsCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Condensed Financial Statements, Captions [Line Items]</link:label>
    <link:label id="lab_srt_CondensedFinancialStatementsCaptionsLineItems_label_en-US" xlink:label="lab_srt_CondensedFinancialStatementsCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Financial Statements, Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CondensedFinancialStatementsCaptionsLineItems" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CondensedFinancialStatementsCaptionsLineItems"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019bdcae-e1a3-769e-8c34-1e158e39dd0b_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_019bdcae-e2e9-797e-94cf-ae4630346fe9_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 10 years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_019bdcae-e2e9-73d2-a31c-3da1370729bc_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Gross deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_019bdcae-e261-761d-acaf-b01a73e1a956_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_us-gaap_PledgingPurposeDomain_label_en-US" xlink:label="lab_us-gaap_PledgingPurposeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTable" xlink:to="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019bdcae-e261-7b8e-8c6c-8a1f78e9b573_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_019bdcae-e1a3-744a-a045-e97b7b89412e_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Interest Income after Provision for Credit Losses</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), after Provision for Loan Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e2e9-757e-822e-755773cc177d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, accrued interest, before allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_TelephoneExpense_019bdcae-e260-78a9-b4cf-adb9f477382c_terseLabel_en-US" xlink:label="lab_fgbi_TelephoneExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Telephone</link:label>
    <link:label id="lab_fgbi_TelephoneExpense_label_en-US" xlink:label="lab_fgbi_TelephoneExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Telephone Expense</link:label>
    <link:label id="lab_fgbi_TelephoneExpense_documentation_en-US" xlink:label="lab_fgbi_TelephoneExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Telephone Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_TelephoneExpense" xlink:href="fgbi-20251231.xsd#fgbi_TelephoneExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_TelephoneExpense" xlink:to="lab_fgbi_TelephoneExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019bdcae-e2e9-7541-a949-63344e6f443c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_019bdcae-e1a3-7b28-b034-d92704ca658f_verboseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:to="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019bdcae-e2e9-78c6-9e0c-b6923e62c2c4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_019bdcae-e261-7586-a388-103ab6f57c91_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease payments</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NonRealEstatePortfolioSegmentMember_019bdcae-e2e9-7c9b-ad41-53a2f3ff12a6_terseLabel_en-US" xlink:label="lab_fgbi_NonRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Real Estate:</link:label>
    <link:label id="lab_fgbi_NonRealEstatePortfolioSegmentMember_label_en-US" xlink:label="lab_fgbi_NonRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Real Estate Portfolio Segment [Member]</link:label>
    <link:label id="lab_fgbi_NonRealEstatePortfolioSegmentMember_documentation_en-US" xlink:label="lab_fgbi_NonRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portfolio segment of the company's total financing receivables related to non-real estate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NonRealEstatePortfolioSegmentMember" xlink:href="fgbi-20251231.xsd#fgbi_NonRealEstatePortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NonRealEstatePortfolioSegmentMember" xlink:to="lab_fgbi_NonRealEstatePortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount_019bdcae-e2e9-76d4-9ec4-96f9fb3ed7dc_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 10 years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing_019bdcae-e261-7196-b611-189b1946dbec_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recorded Investment 90 Days Accruing</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, 90 Days or More Past Due, Still Accruing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestment90DaysPastDueAndStillAccruing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019bdcae-e1a3-7c6c-8225-5646a4ae23ac_verboseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_019bdcae-e261-725a-bf66-97d224f021cf_verboseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average rate at year end</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Weighted Average Interest Rate, at Point in Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_019bdcae-e2e9-7fde-8957-bccd4bae04de_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
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    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue_019bdcae-e261-7b56-aabd-338299175fb4_terseLabel_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Past due period after which loans are considered past due</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue_label_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period Past Due after Which Loans are Considered Past Due</link:label>
    <link:label id="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue_documentation_en-US" xlink:label="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to the period past due, after which loans are considered past due.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:href="fgbi-20251231.xsd#fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:to="lab_fgbi_PeriodPastDueAfterWhichLoansAreConsideredPastDue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashUninsuredAmount_019bdcae-e261-745e-b8f2-a86eb1e8302a_terseLabel_en-US" xlink:label="lab_us-gaap_CashUninsuredAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash in excess of insurable limit</link:label>
    <link:label id="lab_us-gaap_CashUninsuredAmount_label_en-US" xlink:label="lab_us-gaap_CashUninsuredAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Uninsured Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashUninsuredAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashUninsuredAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashUninsuredAmount" xlink:to="lab_us-gaap_CashUninsuredAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019c7b9f-9d36-72eb-9cac-f6d2ce00019a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RisksAndUncertaintiesAbstract_019bdcae-e261-7d89-b266-492659d03711_terseLabel_en-US" xlink:label="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Abstract]</link:label>
    <link:label id="lab_us-gaap_RisksAndUncertaintiesAbstract_label_en-US" xlink:label="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Risks and Uncertainties [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RisksAndUncertaintiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RisksAndUncertaintiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RisksAndUncertaintiesAbstract" xlink:to="lab_us-gaap_RisksAndUncertaintiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019bdcae-e261-7cad-9762-da8689a1f3bc_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019bdcae-e2e9-7da7-845d-33a1db2a5346_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3: Significant Unobservable Inputs</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019bdcae-e2e9-7d80-98d5-3c4d12602e3d_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_019bdcae-e2e9-764d-a2f3-b23da09023fc_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm_019bdcae-e2e9-7ac1-82d7-82795c6f06e2_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term advances from Federal Home Loan Bank</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Federal Home Loan Bank Advances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesLongTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_019bdcae-e2e9-7e51-90e0-ad98055ef9b4_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FederalFarmCreditBankFfcbMember_019bdcae-e2e9-7332-8159-9fa5ceedd3c9_terseLabel_en-US" xlink:label="lab_fgbi_FederalFarmCreditBankFfcbMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Farm Credit Bank (FFCB)</link:label>
    <link:label id="lab_fgbi_FederalFarmCreditBankFfcbMember_label_en-US" xlink:label="lab_fgbi_FederalFarmCreditBankFfcbMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Farm Credit Bank (FFCB) [Member]</link:label>
    <link:label id="lab_fgbi_FederalFarmCreditBankFfcbMember_documentation_en-US" xlink:label="lab_fgbi_FederalFarmCreditBankFfcbMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Institution backed by the government to manage and merge the financing transactions of the Federal Intermediate Credit Banks and the Federal Land Banks. The institution must abide by rules set forth in the Farm Credit Act, which are enforced by an independent federal regulatory agency.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FederalFarmCreditBankFfcbMember" xlink:href="fgbi-20251231.xsd#fgbi_FederalFarmCreditBankFfcbMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FederalFarmCreditBankFfcbMember" xlink:to="lab_fgbi_FederalFarmCreditBankFfcbMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019bdcae-e261-7fc3-8bed-44634b68e385_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_019bdcae-e2e9-72a8-ae72-0b10edb68a27_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss contingency, accrued</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingContractsMember_019bdcae-e2e9-7cc5-9378-aec954104ffb_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingContractsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan servicing assets</link:label>
    <link:label id="lab_us-gaap_ServicingContractsMember_label_en-US" xlink:label="lab_us-gaap_ServicingContractsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Contracts [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingContractsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingContractsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingContractsMember" xlink:to="lab_us-gaap_ServicingContractsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff_019bdcae-e1a3-7dfb-99ce-c8856efa4a29_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated write off, year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio_019bdcae-e2e9-7a5d-b27e-e2360a526b96_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans (including fees)</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Loan and Lease, Held-in-Portfolio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus_019bdcae-e261-7a0e-ad29-72541bbb21d4_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable average recorded investment nonaccrual status</link:label>
    <link:label id="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus_label_en-US" xlink:label="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Average Recorded Investment Nonaccrual Status</link:label>
    <link:label id="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Average recorded investment in financing receivables after undergoing trouble debt restructuring that are on nonaccrual status as of the balance sheet date.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:to="lab_fgbi_FinancingReceivableAverageRecordedInvestmentNonaccrualStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember_019bdcae-e261-7a31-abb1-a0cc2b8fdade_terseLabel_en-US" xlink:label="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property Casualty Insurance And Health Insurance To Centurion Insurance</link:label>
    <link:label id="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember_label_en-US" xlink:label="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Casualty Insurance And Health Insurance To Centurion Insurance [Member]</link:label>
    <link:label id="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember_documentation_en-US" xlink:label="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Casualty Insurance And Health Insurance To Centurion Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:href="fgbi-20251231.xsd#fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:to="lab_fgbi_PropertyCasualtyInsuranceAndHealthInsuranceToCenturionInsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember_019bdcae-e261-73d5-81c8-c0e539d7f6d1_terseLabel_en-US" xlink:label="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lawsuit Alleging Fault For a Loss Of Funds</link:label>
    <link:label id="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember_label_en-US" xlink:label="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lawsuit Alleging Fault For a Loss Of Funds [Member]</link:label>
    <link:label id="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember_documentation_en-US" xlink:label="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lawsuit Alleging Fault For a Loss Of Funds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:href="fgbi-20251231.xsd#fgbi_LawsuitAllegingFaultForALossOfFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:to="lab_fgbi_LawsuitAllegingFaultForALossOfFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NonFarmNonResidentialMember_019bdcae-e1a3-7bb1-bd1b-0d99c675e64a_verboseLabel_en-US" xlink:label="lab_fgbi_NonFarmNonResidentialMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-farm non-residential</link:label>
    <link:label id="lab_fgbi_NonFarmNonResidentialMember_019bdcae-e1a3-7510-a7b2-9ec3ce78f881_terseLabel_en-US" xlink:label="lab_fgbi_NonFarmNonResidentialMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-farm non-residential</link:label>
    <link:label id="lab_fgbi_NonFarmNonResidentialMember_label_en-US" xlink:label="lab_fgbi_NonFarmNonResidentialMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non Farm Non Residential [Member]</link:label>
    <link:label id="lab_fgbi_NonFarmNonResidentialMember_documentation_en-US" xlink:label="lab_fgbi_NonFarmNonResidentialMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the purchase of non-farm non-residential real property.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NonFarmNonResidentialMember" xlink:href="fgbi-20251231.xsd#fgbi_NonFarmNonResidentialMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NonFarmNonResidentialMember" xlink:to="lab_fgbi_NonFarmNonResidentialMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeverageRatiosAbstract_019bdcae-e261-7482-a5e5-aee822a3c8f7_verboseLabel_en-US" xlink:label="lab_us-gaap_LeverageRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 Leverage Capital, Ratio</link:label>
    <link:label id="lab_us-gaap_LeverageRatiosAbstract_label_en-US" xlink:label="lab_us-gaap_LeverageRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Leverage Ratio [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeverageRatiosAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeverageRatiosAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeverageRatiosAbstract" xlink:to="lab_us-gaap_LeverageRatiosAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019bdcae-e1a3-7aa4-8cf9-1e3243827761_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (Loss) Income Available to Common Shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherAbstract_019bdcae-e2e9-7dad-a118-5c028aa10cd3_verboseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other noninterest expense:</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeOtherAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncomeOtherAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeOtherAbstract" xlink:to="lab_us-gaap_NoninterestIncomeOtherAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019bdcae-e1a3-7954-9d35-460d454ac82b_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019bdcae-e1a3-7472-9e8b-fdb9ad01106f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstate_019bdcae-e1a3-7f2d-bd89-bfaaf548a691_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate purchase price</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfRealEstate" xlink:to="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherExpensesAbstract_019bdcae-e2e9-7472-99be-17e8c1f40a7e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Expenses [Abstract]</link:label>
    <link:label id="lab_us-gaap_OtherExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OtherExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherExpensesAbstract" xlink:to="lab_us-gaap_OtherExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019bdcae-e2e9-76d2-a773-bc7beeb66dc7_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019bdcae-e260-7aa2-9232-624675cbf6d1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1: Quoted Prices in Active Markets For Identical Assets</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019bdcae-e260-7359-b819-57068dd8b8c4_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDispositionOfAssets1_019bdcae-e1a3-785d-b795-63b61cfe89a6_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDispositionOfAssets1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (losses) gains on sale of assets</link:label>
    <link:label id="lab_us-gaap_GainLossOnDispositionOfAssets1_label_en-US" xlink:label="lab_us-gaap_GainLossOnDispositionOfAssets1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDispositionOfAssets1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDispositionOfAssets1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDispositionOfAssets1" xlink:to="lab_us-gaap_GainLossOnDispositionOfAssets1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019bdcae-e1a3-7bf4-be3f-7e972f1ef10a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDepositLiabilities_019bdcae-e1a3-7a2c-8465-71c52e610786_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposit from related party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDepositLiabilities_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Deposit Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDepositLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDepositLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDepositLiabilities" xlink:to="lab_us-gaap_RelatedPartyDepositLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock_019bdcae-e260-78ee-ab55-86c5f5f28941_terseLabel_en-US" xlink:label="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Short-term Borrowings</link:label>
    <link:label id="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock_label_en-US" xlink:label="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Short term Borrowings [Table Text Block]</link:label>
    <link:label id="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock_documentation_en-US" xlink:label="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of short-term borrowings arrangements (having initial terms of repayment within one year or the normal operating cycle).</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_ScheduleOfShortTermBorrowingsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:to="lab_fgbi_ScheduleOfShortTermBorrowingsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019bdcae-e261-7b59-96c0-a8de49c61cfc_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through 10 years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_019bdcae-e2e9-747e-8447-ae87558d7077_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount of financing receivable modified in period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Modified in Period, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OtherExpensesTextBlock_019bdcae-e2e9-77c3-a93a-46390a20e236_verboseLabel_en-US" xlink:label="lab_fgbi_OtherExpensesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Expenses</link:label>
    <link:label id="lab_fgbi_OtherExpensesTextBlock_label_en-US" xlink:label="lab_fgbi_OtherExpensesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Expenses [Text Block]</link:label>
    <link:label id="lab_fgbi_OtherExpensesTextBlock_documentation_en-US" xlink:label="lab_fgbi_OtherExpensesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The entire disclosure of other expenses.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OtherExpensesTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_OtherExpensesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OtherExpensesTextBlock" xlink:to="lab_fgbi_OtherExpensesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_019cf6a8-98e0-76cc-8a78-ba5030ec98d4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, State and Local, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_019bdcae-e261-7512-bc50-0a22dff3e168_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_019bdcae-e261-7060-9c11-60cdd51cfcad_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorLocation" xlink:to="lab_dei_AuditorLocation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CoreDepositsMember_019bdcae-e261-7b75-be8e-2ac5e5b5933d_verboseLabel_en-US" xlink:label="lab_us-gaap_CoreDepositsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Core Deposits</link:label>
    <link:label id="lab_us-gaap_CoreDepositsMember_019bdcae-e261-7166-8129-24b432172da4_terseLabel_en-US" xlink:label="lab_us-gaap_CoreDepositsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core deposit intangibles</link:label>
    <link:label id="lab_us-gaap_CoreDepositsMember_label_en-US" xlink:label="lab_us-gaap_CoreDepositsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Core Deposits [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CoreDepositsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CoreDepositsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CoreDepositsMember" xlink:to="lab_us-gaap_CoreDepositsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses_019cf6b4-ec61-77d3-a6ef-ff5f10c7ec22_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment not deductible</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Impairment Losses, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:to="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_019bdcae-e260-73fc-9396-7161fbaa879f_terseLabel_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extended Maturity</link:label>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_label_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extended Maturity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtendedMaturityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ExtendedMaturityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtendedMaturityMember" xlink:to="lab_us-gaap_ExtendedMaturityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind_019c7ac6-72eb-7e05-aa80-d4974386c66e_terseLabel_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued for payment-in-kind</link:label>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind_label_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Issued As Payment-In-Kind</link:label>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind_documentation_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Issued As Payment-In-Kind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:href="fgbi-20251231.xsd#fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:to="lab_fgbi_StockIssuedDuringPeriodValueIssuedAsPaymentInKind" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_TierOneRiskBasedRatiosAbstract_019bdcae-e2e9-7815-9d7c-31d01cfc44a9_verboseLabel_en-US" xlink:label="lab_fgbi_TierOneRiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 Capital, Ratio</link:label>
    <link:label id="lab_fgbi_TierOneRiskBasedRatiosAbstract_label_en-US" xlink:label="lab_fgbi_TierOneRiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tier One Risk Based Ratios [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_TierOneRiskBasedRatiosAbstract" xlink:href="fgbi-20251231.xsd#fgbi_TierOneRiskBasedRatiosAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_TierOneRiskBasedRatiosAbstract" xlink:to="lab_fgbi_TierOneRiskBasedRatiosAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_019bdcae-e1a3-7a59-a800-e47e029ff58e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_019bdcae-e261-74f8-9ae0-1d7148f8b513_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019bdcae-e261-7ee0-9a0c-b43896d536e0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019cfaf9-e28d-7021-80d1-f0ef4e6aee3e_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearOne_019bdcae-e261-7690-93e6-6b249fbc2b58_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearOne_label_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposit Maturities, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositMaturitiesYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDepositMaturitiesYearOne" xlink:to="lab_us-gaap_TimeDepositMaturitiesYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsToExtendCreditMember_019bdcae-e2e9-709a-8a95-287f19b54ce5_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsToExtendCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments to Extend Credit</link:label>
    <link:label id="lab_us-gaap_CommitmentsToExtendCreditMember_label_en-US" xlink:label="lab_us-gaap_CommitmentsToExtendCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments to Extend Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsToExtendCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsToExtendCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsToExtendCreditMember" xlink:to="lab_us-gaap_CommitmentsToExtendCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_StandAloneBranchMember_019bdcae-e2e9-73ea-b832-d916b419c8e2_terseLabel_en-US" xlink:label="lab_fgbi_StandAloneBranchMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stand-Alone Branch</link:label>
    <link:label id="lab_fgbi_StandAloneBranchMember_label_en-US" xlink:label="lab_fgbi_StandAloneBranchMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stand-Alone Branch [Member]</link:label>
    <link:label id="lab_fgbi_StandAloneBranchMember_documentation_en-US" xlink:label="lab_fgbi_StandAloneBranchMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stand-Alone Branch</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_StandAloneBranchMember" xlink:href="fgbi-20251231.xsd#fgbi_StandAloneBranchMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_StandAloneBranchMember" xlink:to="lab_fgbi_StandAloneBranchMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019bdcae-e261-7ff5-a067-6c8697c07be9_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">December 31, 2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019bdcae-e2e9-7249-bdf4-ccb41a767c04_totalLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Subtotal</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_019bdcae-e1a3-736d-890e-17ed5cc71e89_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_019bdcae-e2e9-79bb-bd2f-307fbcd41a35_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Premises and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019bdcae-e261-7e2e-a943-60ac96646ffb_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
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    <link:label id="lab_srt_SubsidiariesMember_019bdcae-e261-75f6-be33-22ace3a34c50_terseLabel_en-US" xlink:label="lab_srt_SubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Bank</link:label>
    <link:label id="lab_srt_SubsidiariesMember_label_en-US" xlink:label="lab_srt_SubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiaries [Member]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_019bdcae-e261-731f-8d19-aa177a5c659d_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Actual and Required Capital Amounts and Ratios</link:label>
    <link:label id="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Compliance with Regulatory Capital Requirements under Banking Regulations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e261-77fc-a892-f8eb02afdffd_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans, net of unearned income</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e261-7409-b970-d35d901b137b_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Loans Net of Unearned Income</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e261-7726-973f-10b102b3637c_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Loans Net of Unearned Income</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable_019bdcae-e2e9-78da-ae8a-091f3ad7800a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Off-balance Sheet Risks [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, off-Balance-Sheet Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTable"/>
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    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_019bdcae-e261-7b00-889b-95a59926ad77_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_019bdcae-e261-781a-a509-cf33f8240a0e_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchase"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_019bdcae-e260-735a-81a5-06839c6a6b94_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unrealized Loss on Investments</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueTableTextBlock"/>
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    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
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    <link:label id="lab_us-gaap_NoncumulativePreferredStockMember_019bdcae-e2e9-74a2-8dfa-baadc53e7cb4_terseLabel_en-US" xlink:label="lab_us-gaap_NoncumulativePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depositary Shares (each representing a 1/40th interest in a share of 6.75% Series A Fixed-Rate Non-Cumulative perpetual preferred stock)</link:label>
    <link:label id="lab_us-gaap_NoncumulativePreferredStockMember_label_en-US" xlink:label="lab_us-gaap_NoncumulativePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncumulative Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncumulativePreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncumulativePreferredStockMember"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_019bdcae-e2e9-70c4-ae07-110b1ccee20c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in other assets and liabilities, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_019bdcae-e260-727a-a500-85b386e0542a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, amounts of transaction</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_019bdcae-e261-7b09-b72b-384574e619ce_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held to maturity, allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent_019bdcae-e261-70bd-8022-a0412bd4c500_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains (losses) on available-for-sale securities included in AOCI , net of applicable income taxes</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Available-for-Sale Securities Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_019bdcae-e261-7571-bba6-215925ea9437_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premises and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_019bdcae-e261-7c89-81a5-d4600efa2724_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net book value</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
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    <link:label id="lab_fgbi_SoftwareExpenseAndAmortization_documentation_en-US" xlink:label="lab_fgbi_SoftwareExpenseAndAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of expenses for software and for amortization of software costs during the period.</link:label>
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    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019bdcae-e1a3-7136-8249-7816d7bbf264_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_019bdcae-e261-7773-8be1-8b37b7b9d27f_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_019bdcae-e2e9-74f5-bb5e-47b1f44323df_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit exposure of loan portfolio by specific credit ratings [Abstract]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, by Origination Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019bdcae-e1a3-7e4f-b6b5-acd9fd94d14f_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CenturionInsuranceMember_019bdcae-e2e9-738a-885d-f9c011347f27_terseLabel_en-US" xlink:label="lab_fgbi_CenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Centurion Insurance</link:label>
    <link:label id="lab_fgbi_CenturionInsuranceMember_label_en-US" xlink:label="lab_fgbi_CenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Centurion Insurance [Member]</link:label>
    <link:label id="lab_fgbi_CenturionInsuranceMember_documentation_en-US" xlink:label="lab_fgbi_CenturionInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Centurion Insurance [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CenturionInsuranceMember" xlink:href="fgbi-20251231.xsd#fgbi_CenturionInsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CenturionInsuranceMember" xlink:to="lab_fgbi_CenturionInsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_019bdcae-e1a3-7619-9fe3-8da01d7aea40_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_019bdcae-e261-7330-9f01-dc78563ec0de_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal income taxes at statutory rate</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
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    <link:label id="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract_019bdcae-e261-74da-a912-764cea842c13_terseLabel_en-US" xlink:label="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">As % of Category</link:label>
    <link:label id="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract_label_en-US" xlink:label="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Net of Deferred Income, Percentage of Category [Abstract]</link:label>
    <link:label id="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract_documentation_en-US" xlink:label="lab_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Net of Deferred Income, Percentage of Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract" xlink:href="fgbi-20251231.xsd#fgbi_LoansAndLeasesReceivableNetOfDeferredIncomePercentageOfCategoryAbstract"/>
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    <link:label id="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio_019bdcae-e2e9-7c97-98fe-66f21b3a7645_terseLabel_en-US" xlink:label="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses on debt securities in continuous loss position as percentage of amortized cost basis of investment securities portfolio</link:label>
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    <link:label id="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to accumulated unrealized loss on investments in debt securities in a continuous loss position as percentage of investment securities portfolio.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio" xlink:href="fgbi-20251231.xsd#fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio" xlink:to="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfInvestmentSecuritiesPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019bdcae-e2e9-75d7-847d-f22fc24f8f4d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019bdcae-e2e9-7301-b956-7b72aac401ca_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt Security [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsGrossAbstract_019bdcae-e260-7c5a-bdb1-aeb89b9c8475_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGrossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets:</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGrossAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGrossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGrossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGrossAbstract"/>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019bdcae-e2e9-7ce2-be40-32ff05ab5445_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Condensed Balance Sheets [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
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    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ExecutiveCategoryAxis"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_019bdcae-e1a3-7fff-b6cc-89ebdd18a34e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">12 Months or More, Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019bdcae-e1a3-7a04-a56b-69476b7ae011_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
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    <link:label id="lab_us-gaap_PassMember_label_en-US" xlink:label="lab_us-gaap_PassMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pass [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_019bdcae-e2e9-7c91-bb66-72e52b3fd8f2_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total, Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_019bdcae-e2e9-73b3-8846-0b1212d43e83_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_019bdcae-e261-781a-97e8-34e17076f1b7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from issuance of common stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Preferred Stock and Preference Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_019bdcae-e261-7bda-95a1-96ecd3347dda_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019bdcae-e2e9-7b14-9fb7-1332de26cd71_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate_019bdcae-e261-7569-84b8-b99c5d525c2b_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank advances</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_019bdcae-e2e9-7254-be3b-e020e80a999a_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Past due Financing Receivables</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestBearingDepositLiabilities_019bdcae-e2e9-71f7-8951-fbc3f7f5ee05_terseLabel_en-US" xlink:label="lab_us-gaap_InterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest-bearing demand</link:label>
    <link:label id="lab_us-gaap_InterestBearingDepositLiabilities_label_en-US" xlink:label="lab_us-gaap_InterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest-Bearing Deposit Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestBearingDepositLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDepositLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestBearingDepositLiabilities" xlink:to="lab_us-gaap_InterestBearingDepositLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_019bdcae-e261-7e88-b365-327dd92226f8_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019bdcae-e2e9-7646-a7ee-cbff63f66b38_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided By Financing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_TierOneLeverageCapitalAbstract_019bdcae-e261-7b86-a813-19c0bc3a166a_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 Leverage Capital, Amount</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneLeverageCapitalAbstract" xlink:to="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019bdcae-e261-76c9-b321-a903f525adba_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_019d308d-a9c0-7a03-a973-015dcb517ed3_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain" xlink:to="lab_us-gaap_DisposalGroupClassificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAbstract_019bdcae-e261-7833-a83f-420ba0ee4b7a_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held to maturity:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value to Amortized Cost, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesAbstract"/>
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    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_019bdcae-e261-72d3-945f-6ee143225a36_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer Portfolio Segment</link:label>
    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsumerPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:to="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FarmlandMember_019bdcae-e261-746c-9b12-bdaf4e61315e_terseLabel_en-US" xlink:label="lab_fgbi_FarmlandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmland</link:label>
    <link:label id="lab_fgbi_FarmlandMember_label_en-US" xlink:label="lab_fgbi_FarmlandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Farmland [Member]</link:label>
    <link:label id="lab_fgbi_FarmlandMember_documentation_en-US" xlink:label="lab_fgbi_FarmlandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the purchase of farmland or the development of land.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FarmlandMember" xlink:href="fgbi-20251231.xsd#fgbi_FarmlandMember"/>
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    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_us-gaap_CapitalAbstract_019bdcae-e260-7826-a502-0238cdb1d365_verboseLabel_en-US" xlink:label="lab_us-gaap_CapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Risk-based Capital, Amount</link:label>
    <link:label id="lab_us-gaap_CapitalAbstract_label_en-US" xlink:label="lab_us-gaap_CapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalAbstract" xlink:to="lab_us-gaap_CapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019bdcae-e2e9-7698-965c-ae5c7d069ebd_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_019bdcae-e2e9-7767-86a6-29c61065c319_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated write off, year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FloatingRateLoansMember_019bdcae-e261-78ee-89d0-5f58acce4be8_verboseLabel_en-US" xlink:label="lab_fgbi_FloatingRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Floating</link:label>
    <link:label id="lab_fgbi_FloatingRateLoansMember_label_en-US" xlink:label="lab_fgbi_FloatingRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Floating Rate Loans [Member]</link:label>
    <link:label id="lab_fgbi_FloatingRateLoansMember_documentation_en-US" xlink:label="lab_fgbi_FloatingRateLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the floating rate loans.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FloatingRateLoansMember" xlink:href="fgbi-20251231.xsd#fgbi_FloatingRateLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FloatingRateLoansMember" xlink:to="lab_fgbi_FloatingRateLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_019bdcae-e261-7c9d-949d-b974d3110f80_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed Securities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward_019bdcae-e261-748d-b83d-cc2163ee600f_terseLabel_en-US" xlink:label="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance For Loan And Lease Losses And Off-Balance-Sheet, Credit Loss, Liability [Roll Forward]</link:label>
    <link:label id="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward_label_en-US" xlink:label="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance For Loan And Lease Losses And Off-Balance-Sheet, Credit Loss, Liability [Roll Forward]</link:label>
    <link:label id="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward_documentation_en-US" xlink:label="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance For Loan And Lease Losses And Off-Balance-Sheet, Credit Loss, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:href="fgbi-20251231.xsd#fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:to="lab_fgbi_AllowanceForLoanAndLeaseLossesAndOffBalanceSheetCreditLossLiabilityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent_019bdcae-e2e9-7d67-b450-f084d83563c6_terseLabel_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferment percentage of base salary, minimum</link:label>
    <link:label id="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent_label_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Minimum Annual Contributions Per Employee, Percent</link:label>
    <link:label id="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent_documentation_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Minimum percentage of employee gross pay the employee may contribute to a defined contribution plan.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:href="fgbi-20251231.xsd#fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:to="lab_fgbi_DefinedContributionPlanMinimumAnnualContributionsPerEmployeePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019bdcae-e2e9-78bf-9e7b-299fdcf2bead_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019bdcae-e1a3-741d-b680-01a508ba52d9_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average lease term (in years)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019bdcae-e2e9-77da-af49-352e8e8edd7d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_019bdcae-e261-7dd4-baa5-8c980b3291a9_verboseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForLoanAndLeaseLossesRollForward_019bdcae-e2e9-7e7f-bb9c-5454669fe17c_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForLoanAndLeaseLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Loan and Lease Losses [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AllowanceForLoanAndLeaseLossesRollForward_label_en-US" xlink:label="lab_us-gaap_AllowanceForLoanAndLeaseLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Loan and Lease Losses [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForLoanAndLeaseLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForLoanAndLeaseLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForLoanAndLeaseLossesRollForward" xlink:to="lab_us-gaap_AllowanceForLoanAndLeaseLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityPublicFloat_019bdcae-e2e9-79e4-b71f-57f19da2d388_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityPublicFloat"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityPublicFloat" xlink:to="lab_dei_EntityPublicFloat" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_EquityBonusPlanMember_019bdcae-e1a3-7a34-a2b0-a2a7f8082207_terseLabel_en-US" xlink:label="lab_fgbi_EquityBonusPlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Bonus Plan</link:label>
    <link:label id="lab_fgbi_EquityBonusPlanMember_label_en-US" xlink:label="lab_fgbi_EquityBonusPlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Bonus Plan [Member]</link:label>
    <link:label id="lab_fgbi_EquityBonusPlanMember_documentation_en-US" xlink:label="lab_fgbi_EquityBonusPlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Bonus Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_EquityBonusPlanMember" xlink:href="fgbi-20251231.xsd#fgbi_EquityBonusPlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_EquityBonusPlanMember" xlink:to="lab_fgbi_EquityBonusPlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_019bdcae-e2e9-7fef-8c9d-1e34ece6c6c5_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_019bdcae-e2e9-71a5-977c-c8dfd06dfd80_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019bdcae-e2e9-78f4-b4e5-7880ed39ad30_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions_019bdcae-e2e9-7cf1-b08a-8c4a4ab892e2_totalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Number of Securities</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-to-Maturity, Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_019bdcae-e1a3-7628-a65c-3b9f3428970e_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed securities</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStock_019bdcae-e260-7940-a8b8-3ff52eaec15c_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStock_019bdcae-e260-7364-acb2-fa5a6ce53929_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStock_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStock" xlink:to="lab_us-gaap_DividendsPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum_019bdcae-e2e9-794d-a280-d7e372dad336_terseLabel_en-US" xlink:label="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of outstanding capital stock, maximum</link:label>
    <link:label id="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum_label_en-US" xlink:label="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage of outstanding capital stock maximum</link:label>
    <link:label id="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum_documentation_en-US" xlink:label="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to maximum percentage of outstanding capital stock for dividends may not be paid.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:href="fgbi-20251231.xsd#fgbi_PercentageOfOutstandingCapitalStockMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:to="lab_fgbi_PercentageOfOutstandingCapitalStockMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_019bdcae-e260-754c-ae99-0b8a34d8eee4_terseLabel_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_label_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PledgingPurposeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgingPurposeAxis" xlink:to="lab_us-gaap_PledgingPurposeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DisposalGroupDepositPremiumPercentage_019d3094-868e-7dd8-9ac0-7b6f0b1d30f2_terseLabel_en-US" xlink:label="lab_fgbi_DisposalGroupDepositPremiumPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposit premium percentage</link:label>
    <link:label id="lab_fgbi_DisposalGroupDepositPremiumPercentage_label_en-US" xlink:label="lab_fgbi_DisposalGroupDepositPremiumPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Deposit Premium, Percentage</link:label>
    <link:label id="lab_fgbi_DisposalGroupDepositPremiumPercentage_documentation_en-US" xlink:label="lab_fgbi_DisposalGroupDepositPremiumPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Deposit Premium, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DisposalGroupDepositPremiumPercentage" xlink:href="fgbi-20251231.xsd#fgbi_DisposalGroupDepositPremiumPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DisposalGroupDepositPremiumPercentage" xlink:to="lab_fgbi_DisposalGroupDepositPremiumPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019bdcae-e1a3-752c-a94a-cd475e4409e0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019bdcae-e261-7d17-9ded-02b904c16e50_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in earnings</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019bdcae-e261-7b0a-963a-b1c581beef7c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_019bdcae-e1a3-7923-8ca5-a96bd53347dd_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019bdcae-e2e9-7dd5-bff2-927dd785c079_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock $1 Par</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_019c7b38-a3d6-7fd7-b2be-c6a3c109e8a7_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common Stock $1 Par</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestBearingDomesticDepositBrokered_019bdcae-e260-7e88-aa34-654413b6282e_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestBearingDomesticDepositBrokered" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Brokered deposits</link:label>
    <link:label id="lab_us-gaap_InterestBearingDomesticDepositBrokered_label_en-US" xlink:label="lab_us-gaap_InterestBearingDomesticDepositBrokered" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest-Bearing Domestic Deposit, Brokered</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestBearingDomesticDepositBrokered" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDomesticDepositBrokered"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestBearingDomesticDepositBrokered" xlink:to="lab_us-gaap_InterestBearingDomesticDepositBrokered" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans_019bdcae-e261-7b99-8262-c8c70671858f_negatedTerseLabel_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Discount on purchased loans</link:label>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans_label_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities Discount On Purchased Loans</link:label>
    <link:label id="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans_documentation_en-US" xlink:label="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities Discount On Purchased Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:href="fgbi-20251231.xsd#fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:to="lab_fgbi_DeferredTaxLiabilitiesDiscountOnPurchasedLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019bdcae-e2e9-7fd9-83bf-f1582c551e96_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Increase In Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019bdcae-e2e9-7106-b057-3c8b6c15d689_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_019bdcae-e1a3-7809-b4e3-e6ff35423383_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends paid (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_019c7b38-a3d6-7600-bfd9-1be59ec4c6dd_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends on common stock (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OtherRealEstateFairValueDisclosure_019bdcae-e1a3-7657-a81a-1a92e6c36d2d_verboseLabel_en-US" xlink:label="lab_fgbi_OtherRealEstateFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other real estate owned measured at fair value</link:label>
    <link:label id="lab_fgbi_OtherRealEstateFairValueDisclosure_label_en-US" xlink:label="lab_fgbi_OtherRealEstateFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate Fair Value Disclosure</link:label>
    <link:label id="lab_fgbi_OtherRealEstateFairValueDisclosure_documentation_en-US" xlink:label="lab_fgbi_OtherRealEstateFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">This element represents the portion of the balance sheet assertion valued at fair value by the entity whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission. This element represents the fair value of other real estate owned by bank.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OtherRealEstateFairValueDisclosure" xlink:href="fgbi-20251231.xsd#fgbi_OtherRealEstateFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OtherRealEstateFairValueDisclosure" xlink:to="lab_fgbi_OtherRealEstateFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019bdcae-e261-7315-8cc9-8ab6539615b4_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnallocatedFinancingReceivablesMember_019bdcae-e260-731a-8457-f81ccbe0d8b0_terseLabel_en-US" xlink:label="lab_us-gaap_UnallocatedFinancingReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unallocated</link:label>
    <link:label id="lab_us-gaap_UnallocatedFinancingReceivablesMember_label_en-US" xlink:label="lab_us-gaap_UnallocatedFinancingReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unallocated Financing Receivables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnallocatedFinancingReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnallocatedFinancingReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnallocatedFinancingReceivablesMember" xlink:to="lab_us-gaap_UnallocatedFinancingReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_019bdcae-e2e9-7add-9364-499742daafd6_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock_019bdcae-e2e9-7024-b0b1-537e339dcda5_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Condensed Balance Sheets</link:label>
    <link:label id="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock_label_en-US" xlink:label="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Balance Sheet [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfCondensedBalanceSheetTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:to="lab_srt_ScheduleOfCondensedBalanceSheetTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019bdcae-e1a3-7980-8bd8-8f6c89714cf1_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019bdcae-e261-78f5-b033-2042da6d98a1_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses_019cf6b5-da36-7935-8164-4bcd6dd448eb_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment not deductible</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Impairment Losses, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseImpairmentLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_019bdcae-e2e9-7714-a6db-db511f26041b_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration_019d1b74-2652-7663-8aa6-8758ecc8b8e4_terseLabel_en-US" xlink:label="lab_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Jurisdiction of Domicile [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Jurisdiction of Domicile [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration" xlink:to="lab_us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019bdcae-e1a3-7e3c-b875-72b81f6cea91_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in other comprehensive income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019bdcae-e2e9-7ef7-b64a-a0b707d3ffee_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Decrease) increase in equity in undistributed earnings of subsidiary</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019bdcae-e2e9-7783-9dcd-0ec5159b0f18_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Decrease (increase) in equity in undistributed earnings of subsidiary</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue_019bdcae-e261-79d7-a416-d197c1774cf3_totalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Unrealized Loss Position, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DividendRestrictionsTextBlock_019bdcae-e2e9-7aa8-a534-b241bf4c6925_verboseLabel_en-US" xlink:label="lab_fgbi_DividendRestrictionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Dividend Restrictions</link:label>
    <link:label id="lab_fgbi_DividendRestrictionsTextBlock_label_en-US" xlink:label="lab_fgbi_DividendRestrictionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Restrictions [Text Block]</link:label>
    <link:label id="lab_fgbi_DividendRestrictionsTextBlock_documentation_en-US" xlink:label="lab_fgbi_DividendRestrictionsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The entire disclosure of dividend restrictions.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DividendRestrictionsTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_DividendRestrictionsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DividendRestrictionsTextBlock" xlink:to="lab_fgbi_DividendRestrictionsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_019bdcae-e2e9-798e-b617-267b1a8b29ae_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Without Related Allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, No Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DallasFortWorthTexasMember_019d2ad6-1d5a-7d58-b75c-d83a2fa48838_terseLabel_en-US" xlink:label="lab_fgbi_DallasFortWorthTexasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dallas&#8211;Fort Worth, Texas</link:label>
    <link:label id="lab_fgbi_DallasFortWorthTexasMember_label_en-US" xlink:label="lab_fgbi_DallasFortWorthTexasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dallas&#8211;Fort Worth, Texas [Member]</link:label>
    <link:label id="lab_fgbi_DallasFortWorthTexasMember_documentation_en-US" xlink:label="lab_fgbi_DallasFortWorthTexasMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dallas&#8211;Fort Worth, Texas</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualTable_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableNonaccrualTable"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGross"/>
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    <link:label id="lab_us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff_019bdcae-e261-7fc3-b454-8cebe4932c9d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold period past due for charge-off of loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Threshold Period Past Due, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableThresholdPeriodPastDueWriteoff"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchasesSalesIssuancesSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchasesSalesIssuancesSettlements"/>
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    <link:label id="lab_us-gaap_ShortTermBorrowings_019bdcae-e260-7a0a-8bf8-c9fe75cc937d_totalLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total short-term borrowings</link:label>
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    <link:label id="lab_us-gaap_ShortTermBorrowings_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt</link:label>
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    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearFive_019d3ffa-2890-7b4b-bbca-daaa45f22a07_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearFive_label_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposit Maturities, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositMaturitiesYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearFive"/>
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    <link:label id="lab_us-gaap_DepositsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_DepositsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis"/>
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    <link:label id="lab_us-gaap_CollateralizedMortgageObligationsMember_019bdcae-e2e9-7ab5-ab01-09e01484d9c4_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralizedMortgageObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized mortgage obligations</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff"/>
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    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_019bdcae-e2e9-76ba-b3fc-ee1b63906c99_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_SecuredDebt_019bdcae-e261-720e-b40f-050551d13f00_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior long-term debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebt_label_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebt" xlink:to="lab_us-gaap_SecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019bdcae-e2e9-7870-b281-06cef3ff77cf_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities and Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019bdcae-e2e9-78f9-b6b2-4eab3ab4716e_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
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    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent_019bdcae-e261-7acd-934d-9f0f30340737_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains (losses) reclassified out of AOCI into earnings, net of tax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_019bdcae-e2e9-7a41-8390-22a3c1b01f5b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther"/>
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    <link:label id="lab_fgbi_NonPerformingAssets_019d3080-3242-7b2b-ad28-12483dadecdc_terseLabel_en-US" xlink:label="lab_fgbi_NonPerformingAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-performing assets</link:label>
    <link:label id="lab_fgbi_NonPerformingAssets_label_en-US" xlink:label="lab_fgbi_NonPerformingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Performing Assets</link:label>
    <link:label id="lab_fgbi_NonPerformingAssets_documentation_en-US" xlink:label="lab_fgbi_NonPerformingAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Performing Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NonPerformingAssets" xlink:href="fgbi-20251231.xsd#fgbi_NonPerformingAssets"/>
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    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019bdcae-e1a3-772b-822a-3a274bc9c720_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
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    <link:label id="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss_019bdcae-e261-73a1-a600-906e6b1111ea_terseLabel_en-US" xlink:label="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities in a continuous loss position for over 12 months, unrealized loss</link:label>
    <link:label id="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:label id="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss_documentation_en-US" xlink:label="lab_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of accumulated unrealized loss on investments in debt securities in a continuous loss position.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="fgbi-20251231.xsd#fgbi_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019bdcae-e261-7099-84b1-de14e794888d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lessee, Minimum Lease Payments Under Non-Cancelable Operating Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInDepositsWithOtherFederalHomeLoanBanks_019bdcae-e260-7811-9785-3f4c24d638d9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDepositsWithOtherFederalHomeLoanBanks" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Increase in interest bearing deposits</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDepositsWithOtherFederalHomeLoanBanks" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDepositsWithOtherFederalHomeLoanBanks"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_019bdcae-e260-721b-bb24-7acc11da53c8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated, year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfTradingSecuritiesHeldforinvestment_019bdcae-e261-7055-a2dd-491d223ff636_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfTradingSecuritiesHeldforinvestment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of equity securities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLiability_019bdcae-e1a3-7afc-a883-83d15406b7e3_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019bdcae-e1a3-7c9b-b00c-85fa5c14af2a_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
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    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets_019bdcae-e260-7891-98dd-2bf2a4d47c2e_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital Ratio, Well Capitalized, Minimum</link:label>
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    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_019bdcae-e1a3-7cb5-9091-537787079121_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Government Agencies</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019bdcae-e260-708b-a770-f81057d06e89_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 Days or Greater Past Due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_019bdcae-e2e9-7ac7-adb4-d76aef593367_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityLenderDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:to="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract_019bdcae-e261-75a1-aff7-2c99ee5389f7_verboseLabel_en-US" xlink:label="lab_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Actual and required capital amounts and ratios [Abstract]</link:label>
    <link:label id="lab_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract_label_en-US" xlink:label="lab_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Actual and Required Capital Amounts and Ratios [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract" xlink:href="fgbi-20251231.xsd#fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract" xlink:to="lab_fgbi_ActualAndRequiredCapitalAmountsAndRatiosAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019bdcae-e1a3-7852-a2a5-06f57e88596d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_019bdcae-e261-79dc-8246-58b847275ca4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019c7aab-4c49-7c23-9b7d-3bc70828d06e_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_019bdcae-e260-7266-a83e-786be72afc97_verboseLabel_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Capital Requirements</link:label>
    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_label_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Capital Requirements under Banking Regulations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:to="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_019bdcae-e2e9-7026-94b6-df2873f24445_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated, year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019bdcae-e261-7999-86f5-22ded04427c2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Condensed Statements of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Cash_019bdcae-e2e9-730d-953f-22904b5d06a5_terseLabel_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_Cash_label_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Cash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Cash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Cash" xlink:to="lab_us-gaap_Cash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019bdcae-e260-75ae-a365-161fa78259ea_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_019bdcae-e1a3-7ac1-91c3-82ba121c30d6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets_019bdcae-e261-76cd-8a85-bfbdbe078eb5_verboseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital Ratio, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:to="lab_us-gaap_TierOneRiskBasedCapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019bdcae-e261-7c06-adfa-c267e6fb04ef_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (Loss) Income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan_019c5628-2272-7769-b233-4f7a058ac611_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individually evaluated loans, collateral dependent loan</link:label>
    <link:label id="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan_label_en-US" xlink:label="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Individually Evaluated for Credit Loss, Collateral Dependent Loan</link:label>
    <link:label id="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Individually Evaluated for Credit Loss, Collateral Dependent Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:to="lab_fgbi_FinancingReceivableIndividuallyEvaluatedForCreditLossCollateralDependentLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019bdcae-e1a3-7327-9f42-91d28180674b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_019bdcae-e1a3-71d5-83f6-aecfd722333a_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Long-term Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeposits_019bdcae-e261-7680-ab59-4dac0ed7356d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase in deposits</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDeposits_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDeposits" xlink:to="lab_us-gaap_IncreaseDecreaseInDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualStatusLineItems_019bdcae-e2e9-7ab9-89c0-8aff5829df02_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualStatusLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualStatusLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualStatusLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualStatusLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableNonaccrualStatusLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableNonaccrualStatusLineItems" xlink:to="lab_us-gaap_FinancingReceivableNonaccrualStatusLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess_019bdcae-e1a3-7c47-b825-4b5facd7ef56_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One year or less</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess_label_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing receivables that are maturing after one year or less</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing receivables, excluding nonaccrual status notes, gross carrying amount that are maturing after one year or less.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:to="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearOrLess" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure_019bdcae-e1a3-76da-9f89-84beb6894692_terseLabel_en-US" xlink:label="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term advances from Federal Home Loan Bank</link:label>
    <link:label id="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure_label_en-US" xlink:label="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long Term Advances From Federal Home Loan Bank, Fair Value Disclosure</link:label>
    <link:label id="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure_documentation_en-US" xlink:label="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long Term Advances From Federal Home Loan Bank, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:href="fgbi-20251231.xsd#fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:to="lab_fgbi_LongTermAdvancesFromFederalHomeLoanBankFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract_019bdcae-e2e9-7bfe-bd98-f76de3cfa59d_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for sale:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities, Debt Maturities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019bdcae-e260-7239-aa2b-da81308d6b66_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt outstanding</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019bdcae-e260-7230-8002-1a0cb7c2977b_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019bdcae-e261-7d37-8017-1384fa2a3005_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019bdcae-e261-7387-b967-30a6d21b8fb9_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock_019bdcae-e261-7494-9506-b2e3b84f8009_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Condensed Statements of Cash Flows</link:label>
    <link:label id="lab_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock_label_en-US" xlink:label="lab_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Cash Flow Statement [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfCondensedCashFlowStatementTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock" xlink:to="lab_srt_ScheduleOfCondensedCashFlowStatementTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses_019bdcae-e2e9-79bc-a30c-f0dd67f20839_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Tax Deferred Expense, Reserve and Accrual, Financing Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:to="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019bdcae-e1a3-738d-98af-9b2d260ebba4_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">December 31, 2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateTable_019bdcae-e2e9-7f43-b208-4f18ccc80602_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:label id="lab_us-gaap_RealEstateTable_label_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateTable" xlink:to="lab_us-gaap_RealEstateTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_019bdcae-e260-7f6c-9d85-d186ceb85742_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_019d2ad6-1d5a-7a1b-b900-65806f6f3456_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_019bdcae-e2e9-7c95-9cac-90199abb7511_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019bdcae-e2e9-7359-a25d-5436d6195e11_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows From Operating Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019bdcae-e2e9-7495-9428-afca25417b04_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019bdcae-e261-7fc9-99b7-71ee1bfd6af4_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract_019bdcae-e2e9-7b47-8b2c-c919c625e8d6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (losses) gains on securities:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Available-for-Sale Securities Adjustment, before Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentBeforeTaxPortionAttributableToParentAbstract"/>
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    <link:label id="lab_fgbi_FederalHomeLoanBankFhlbMember_019bdcae-e260-7ac1-93ad-92721245be3b_terseLabel_en-US" xlink:label="lab_fgbi_FederalHomeLoanBankFhlbMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Advances from FHLB</link:label>
    <link:label id="lab_fgbi_FederalHomeLoanBankFhlbMember_label_en-US" xlink:label="lab_fgbi_FederalHomeLoanBankFhlbMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank (FHLB) [Member]</link:label>
    <link:label id="lab_fgbi_FederalHomeLoanBankFhlbMember_documentation_en-US" xlink:label="lab_fgbi_FederalHomeLoanBankFhlbMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">An organization created by the Federal Home Loan Bank Act of 1932 to increase the amount of funds available for lending institutions who provide mortgages and similar loan agreements to individuals.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FederalHomeLoanBankFhlbMember" xlink:to="lab_fgbi_FederalHomeLoanBankFhlbMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_019bdcae-e1a3-7646-82d6-7de9df52b0b6_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings</link:label>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseBorrowings" xlink:to="lab_us-gaap_InterestExpenseBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions_019bdcae-e260-7258-ad86-2e0ef6dde8f5_terseLabel_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of debt securities in continuous loss position for over 12 months</link:label>
    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions_label_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities In Unrealized Loss Positions More Than Twelve Months Qualitative Disclosure Number Of Positions</link:label>
    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions_documentation_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of debt securities that have been in a continuous debt position of unrealized loss position for greater than or equal to a year for which an other-than-temporary impairment (OTTI) has not been recognized in the income statement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:href="fgbi-20251231.xsd#fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:to="lab_fgbi_SecuritiesInUnrealizedLossPositionsMoreThanTwelveMonthsQualitativeDisclosureNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019bdcae-e2e9-72b5-a684-56a1d69d9abc_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfAutomatedTellerMachines_019bdcae-e1a3-70ed-9f83-8cb34cfe571a_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfAutomatedTellerMachines" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of automated teller machines (ATMs)</link:label>
    <link:label id="lab_fgbi_NumberOfAutomatedTellerMachines_label_en-US" xlink:label="lab_fgbi_NumberOfAutomatedTellerMachines" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Automated Teller Machines</link:label>
    <link:label id="lab_fgbi_NumberOfAutomatedTellerMachines_documentation_en-US" xlink:label="lab_fgbi_NumberOfAutomatedTellerMachines" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refer to number of automated teller machines.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfAutomatedTellerMachines" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfAutomatedTellerMachines"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfAutomatedTellerMachines" xlink:to="lab_fgbi_NumberOfAutomatedTellerMachines" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearTwo_019bdcae-e261-7030-829e-7115217b1369_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearTwo_label_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposit Maturities, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositMaturitiesYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDepositMaturitiesYearTwo" xlink:to="lab_us-gaap_TimeDepositMaturitiesYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019bdcae-e261-7e16-8a94-e479ee4f9362_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">December 31, 2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketingExpense_019bdcae-e261-7ff4-acc9-7b20f62d1a1c_terseLabel_en-US" xlink:label="lab_us-gaap_MarketingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketing and public relations</link:label>
    <link:label id="lab_us-gaap_MarketingExpense_label_en-US" xlink:label="lab_us-gaap_MarketingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketingExpense" xlink:to="lab_us-gaap_MarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets_019bdcae-e261-7221-a996-fa7ae3bfc848_verboseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum Capital Requirements</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:to="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseSavingsDeposits_019bdcae-e261-7103-b91d-4df02f20bd61_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings deposits</link:label>
    <link:label id="lab_us-gaap_InterestExpenseSavingsDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Savings Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseSavingsDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseSavingsDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseSavingsDeposits" xlink:to="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_019bdcae-e2e9-7f30-88d3-a9c51f72f6e2_verboseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, fair value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_019bdcae-e2e9-7a4b-96ba-3673dd694264_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_019bdcae-e2e9-7188-bffd-d236bf4cfd26_totalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total held to maturity securities</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_019bdcae-e2e9-7319-9581-2eb7456de816_netLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Securities, held for maturity</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019bdcae-e2e9-7ea3-8fab-c8a2e415045c_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares Outstanding (in shares)</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalizedContractCostNet_019bdcae-e1a3-7281-afed-45a8f8b3c15c_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalizedContractCostNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitalized contract cost</link:label>
    <link:label id="lab_us-gaap_CapitalizedContractCostNet_label_en-US" xlink:label="lab_us-gaap_CapitalizedContractCostNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capitalized Contract Cost, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalizedContractCostNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedContractCostNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalizedContractCostNet" xlink:to="lab_us-gaap_CapitalizedContractCostNet" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_SmithTateInvestmentL.L.C.Member_019bdcae-e1a3-784b-8be0-4f2f488b1b39_terseLabel_en-US" xlink:label="lab_fgbi_SmithTateInvestmentL.L.C.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Smith &amp; Tate Investment, L. L. C.</link:label>
    <link:label id="lab_fgbi_SmithTateInvestmentL.L.C.Member_label_en-US" xlink:label="lab_fgbi_SmithTateInvestmentL.L.C.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Smith &amp; Tate Investment, L. L. C. [Member]</link:label>
    <link:label id="lab_fgbi_SmithTateInvestmentL.L.C.Member_documentation_en-US" xlink:label="lab_fgbi_SmithTateInvestmentL.L.C.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Smith &amp; Tate Investment, L. L. C.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SmithTateInvestmentL.L.C.Member" xlink:href="fgbi-20251231.xsd#fgbi_SmithTateInvestmentL.L.C.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_SmithTateInvestmentL.L.C.Member" xlink:to="lab_fgbi_SmithTateInvestmentL.L.C.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019bdcae-e260-7d9d-92a7-36d53764ba88_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
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    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Common Equity Tier 1 Risk-Based Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonEquityTierOneCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonEquityTierOneCapitalAbstract"/>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
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    <link:label id="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfAllIndividualSecuritiesAmortizedCostBasis_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesContinuousUnrealizedLossPositionAccumulatedLossAsPercentageOfAllIndividualSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to accumulated unrealized loss on investments in debt securities in a continuous loss position as percentage of total individual securities' amortized cost basis.</link:label>
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    <link:label id="lab_us-gaap_TimeDeposits_019bdcae-e2e9-7fa7-8da2-f934ac6d7d77_totalLabel_en-US" xlink:label="lab_us-gaap_TimeDeposits" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDeposits"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019bdcae-e2e9-7185-88b9-74296480e5d1_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonEquityTierOneCapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonEquityTierOneCapitalRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonEquityTierOneCapitalRequiredForCapitalAdequacy" xlink:to="lab_us-gaap_CommonEquityTierOneCapitalRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable_019bdcae-e2e9-7ff5-81e1-25502217dc0e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Troubled Debt Restructuring [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Modified [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableTroubledDebtRestructuringsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_019bdcae-e261-71a4-b6a8-50fdd2cb8de3_terseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_019d1b61-9be0-7465-8453-92dc4600aa5f_verboseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses expense (reversal)</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:to="lab_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock_019bdcae-e1a3-78d8-89c1-7bbc4d43fcb9_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Funds invested in Federal Home Loan Bank stock</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Federal Home Loan Bank Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireFederalHomeLoanBankStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:to="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome_019cf6ae-782d-7dd8-a980-473576f2e402_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax exempt municipal income</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Exempt Income, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxExemptIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:to="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_019bdcae-e2e9-706c-b1c3-838178d99262_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolving"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019bdcae-e2e9-7bc8-8540-a44f46807529_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019bdcae-e261-7460-a797-cc680652d690_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Allowance for Loan Losses and Allowance and Loans Individually and Collectively Evaluated for Impairment</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesMember_019bdcae-e2e9-7a78-a0dc-811a53e901dd_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesMember" xlink:to="lab_us-gaap_MortgagesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy_019bdcae-e1a3-7e18-97c9-b4230586e346_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan fees and costs</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Fee and Interest Income [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableOriginationFeesDiscountsOrPremiumsAndDirectCostsToAcquireLoansPolicy"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019bdcae-e261-75f0-a2f1-25c9bd10386c_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows From Investing Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019bdcae-e261-7e64-9245-e3041374a098_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
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    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_019bdcae-e2e9-7588-af36-a31d897cac09_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionMember_019d1b4d-6996-7fc7-8835-bb2ca2d2692a_terseLabel_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale And Leaseback Transaction</link:label>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionMember_label_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale And Leaseback Transaction [Member]</link:label>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionMember_documentation_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale And Leaseback Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SaleAndLeasebackTransactionMember" xlink:href="fgbi-20251231.xsd#fgbi_SaleAndLeasebackTransactionMember"/>
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    <link:label id="lab_us-gaap_InterestReceivable_019bdcae-e260-77bc-a045-78bf786dcd5b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_019bdcae-e261-7bfe-8a27-3825872b387a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_019bdcae-e261-7e2f-beb9-b1d2522503f0_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease, cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_019bdcae-e2e9-7956-9d75-0b8bffa1149a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019bdcae-e2e9-7cbf-8bee-de5859ea0deb_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_019bdcae-e1a3-7df2-ad24-ac2e7ebdb0cf_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lawsuit alleging fault for a loss of funds with possible loss</link:label>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_label_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Estimate of Possible Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyEstimateOfPossibleLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:to="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_019bdcae-e261-7fdc-9f8d-a663b3adfdad_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lease Cost</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfPropertiesSold_019bdcae-e1a3-70c5-8d74-9af12aba6f8e_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfPropertiesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of properties sold</link:label>
    <link:label id="lab_fgbi_NumberOfPropertiesSold_label_en-US" xlink:label="lab_fgbi_NumberOfPropertiesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Properties Sold</link:label>
    <link:label id="lab_fgbi_NumberOfPropertiesSold_documentation_en-US" xlink:label="lab_fgbi_NumberOfPropertiesSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Properties Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfPropertiesSold" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfPropertiesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfPropertiesSold" xlink:to="lab_fgbi_NumberOfPropertiesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax_019d1b4a-957c-7af8-b6ed-7a8200e5cfe6_terseLabel_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pre-tax gain on sale-leaseback transaction</link:label>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax_label_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale And Leaseback Transaction, Gain (Loss), Before Tax</link:label>
    <link:label id="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax_documentation_en-US" xlink:label="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale And Leaseback Transaction, Gain (Loss), Before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:href="fgbi-20251231.xsd#fgbi_SaleAndLeasebackTransactionGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:to="lab_fgbi_SaleAndLeasebackTransactionGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PublicFundDeposits_019bdcae-e1a3-787f-9892-0c3888066657_terseLabel_en-US" xlink:label="lab_fgbi_PublicFundDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public fund deposits</link:label>
    <link:label id="lab_fgbi_PublicFundDeposits_label_en-US" xlink:label="lab_fgbi_PublicFundDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public fund deposits</link:label>
    <link:label id="lab_fgbi_PublicFundDeposits_documentation_en-US" xlink:label="lab_fgbi_PublicFundDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The carrying amount of the public fund deposits.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PublicFundDeposits" xlink:href="fgbi-20251231.xsd#fgbi_PublicFundDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PublicFundDeposits" xlink:to="lab_fgbi_PublicFundDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_019cf69f-29ae-77d1-9a3c-487111c737ce_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_019bdcae-e260-700f-9b56-e41a06398dc8_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_019bdcae-e2e9-7062-af82-f9cb17ddb19a_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_019bdcae-e261-7fe2-ad61-83bed03aa9c2_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Subtotal</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_019bdcae-e261-7a75-9fc1-8300ebb4324a_verboseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Business and Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation, Basis of Presentation, Business Description and Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019bdcae-e2e9-7ab2-b6cf-df0dd59e25bf_verboseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Paid During the Period:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesPolicy_019bdcae-e2e9-7668-8a9e-393be3a6629f_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesPolicy_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecuritiesPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesPolicy" xlink:to="lab_us-gaap_MarketableSecuritiesPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_019bdcae-e2e9-7af7-9a49-8b8bba674be3_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment_019bdcae-e2e9-7f35-a9b5-bbfc5d8a6d2a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance Collectively Evaluated</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Collectively Evaluated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesCollectivelyEvaluatedForImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019bdcae-e261-7e92-beb6-54366a5c620e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FhlbStockDividends_019c7b9f-9d36-788e-85ac-da954d5dada2_negatedTerseLabel_en-US" xlink:label="lab_fgbi_FhlbStockDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">FHLB stock dividends</link:label>
    <link:label id="lab_fgbi_FhlbStockDividends_label_en-US" xlink:label="lab_fgbi_FhlbStockDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">FHLB stock dividends</link:label>
    <link:label id="lab_fgbi_FhlbStockDividends_documentation_en-US" xlink:label="lab_fgbi_FhlbStockDividends" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustment to operating income to reflect stock dividends received on Federal Home Loan Bank stock.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FhlbStockDividends" xlink:href="fgbi-20251231.xsd#fgbi_FhlbStockDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FhlbStockDividends" xlink:to="lab_fgbi_FhlbStockDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019cf6b8-aa82-73e6-9065-ecf4a2ab18c6_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember_019bdcae-e2e9-780f-a11b-8f195e4e3c54_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate:</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialRealEstatePortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:to="lab_us-gaap_CommercialRealEstatePortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_019bdcae-e261-734b-b9c8-25cb74f74c5b_verboseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Surplus</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019bdcae-e261-74a9-be67-1b2d0824a907_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019bdcae-e261-7cd4-ac5c-07fc5c90cf51_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Cash Provided By (Used In) Investing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019bdcae-e1a3-7574-8da3-81da934bfe50_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest on deposits and borrowed funds</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019bdcae-e261-79cb-96db-9e5779876546_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_019bdcae-e1a3-707d-942e-68a85899c4ca_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityAxis" xlink:to="lab_us-gaap_LineOfCreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019bdcae-e2e9-75f1-9c38-b722f9d5d8d6_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, right-of-use asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense_019bdcae-e260-725d-921e-f1dbf02ec368_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax penalties expense</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits, Income Tax Penalties Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense" xlink:to="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CommercialAndIndustrialMember_019bdcae-e2e9-71c2-85a9-5d9d5dba07a9_terseLabel_en-US" xlink:label="lab_fgbi_CommercialAndIndustrialMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial</link:label>
    <link:label id="lab_fgbi_CommercialAndIndustrialMember_019bdcae-e2e9-73cc-8626-7c84e11986f9_verboseLabel_en-US" xlink:label="lab_fgbi_CommercialAndIndustrialMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial</link:label>
    <link:label id="lab_fgbi_CommercialAndIndustrialMember_label_en-US" xlink:label="lab_fgbi_CommercialAndIndustrialMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial and Industrial [Member]</link:label>
    <link:label id="lab_fgbi_CommercialAndIndustrialMember_documentation_en-US" xlink:label="lab_fgbi_CommercialAndIndustrialMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans issued to commercial and industrial institutions.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CommercialAndIndustrialMember" xlink:href="fgbi-20251231.xsd#fgbi_CommercialAndIndustrialMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CommercialAndIndustrialMember" xlink:to="lab_fgbi_CommercialAndIndustrialMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019cf6bd-49ab-7d7d-81b0-a17217f2a59a_totalLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019bdcae-e260-7e1c-b834-26c2d491a77e_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings_019bdcae-e261-7733-b2dc-07e4f9588cf0_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares used secured pledge borrowings (in shares)</link:label>
    <link:label id="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings_label_en-US" xlink:label="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Shares Used Secured Pledge Borrowings</link:label>
    <link:label id="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings_documentation_en-US" xlink:label="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The number of shares of the Company's interest in a subsidiary used as a secured pledge on a borrowing.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfSharesUsedSecuredPledgeBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:to="lab_fgbi_NumberOfSharesUsedSecuredPledgeBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes_019bdcae-e261-7990-8892-20fa2955dcca_terseLabel_en-US" xlink:label="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxes - sales, capital and franchise</link:label>
    <link:label id="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes_label_en-US" xlink:label="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxesExcludingIncomeAndExciseTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:to="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAbstract_019bdcae-e2e9-7566-b842-abbd2a140baf_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:label id="lab_us-gaap_RealEstateAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAbstract" xlink:to="lab_us-gaap_RealEstateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract_019bdcae-e261-7622-892a-75c436679df1_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OtherRealEstateOwnedTableTextBlock_019bdcae-e261-79d1-9e75-1a214cc7b87b_verboseLabel_en-US" xlink:label="lab_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Other Real Estate Owned</link:label>
    <link:label id="lab_fgbi_OtherRealEstateOwnedTableTextBlock_label_en-US" xlink:label="lab_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other real estate owned [Table Text Block]</link:label>
    <link:label id="lab_fgbi_OtherRealEstateOwnedTableTextBlock_documentation_en-US" xlink:label="lab_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of the change in other real estate on properties owned acquired by foreclosure.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_OtherRealEstateOwnedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:to="lab_fgbi_OtherRealEstateOwnedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_019bdcae-e2e9-78c7-8dbc-20cab36305ee_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and intangible assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_019bdcae-e2e9-7d4f-ad2b-a6e0e88e7220_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bank premises</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019cf6e4-44b1-74db-8fa8-3e27090afc07_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019bdcae-e260-7816-a60b-6d553081db48_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_019bdcae-e2e9-70f0-8b65-435aab5190f6_verboseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasury</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_019bdcae-e2e9-72d5-aac5-1f0ecaba68da_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Government Treasuries (U.S.)</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasurySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasurySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasurySecuritiesMember" xlink:to="lab_us-gaap_USTreasurySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_019cf69e-715a-767a-abc6-fcb582eee21e_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease_019bdcae-e1a3-75d0-aea4-f5cc4b97d156_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (Decrease) Increase</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesPeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InformationTechnologyAndDataProcessing_019bdcae-e2e9-75fd-b574-3b42ef1e22ad_terseLabel_en-US" xlink:label="lab_us-gaap_InformationTechnologyAndDataProcessing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Data processing</link:label>
    <link:label id="lab_us-gaap_InformationTechnologyAndDataProcessing_label_en-US" xlink:label="lab_us-gaap_InformationTechnologyAndDataProcessing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Information Technology and Data Processing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InformationTechnologyAndDataProcessing" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InformationTechnologyAndDataProcessing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InformationTechnologyAndDataProcessing" xlink:to="lab_us-gaap_InformationTechnologyAndDataProcessing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019bdcae-e260-7ff6-a6c7-f396add54840_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PercentageOfEntityDeposits_019bdcae-e1a3-7e2f-a550-584fc3997588_terseLabel_en-US" xlink:label="lab_fgbi_PercentageOfEntityDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of entity deposits</link:label>
    <link:label id="lab_fgbi_PercentageOfEntityDeposits_label_en-US" xlink:label="lab_fgbi_PercentageOfEntityDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percentage of entity deposits</link:label>
    <link:label id="lab_fgbi_PercentageOfEntityDeposits_documentation_en-US" xlink:label="lab_fgbi_PercentageOfEntityDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refer to percentage of entity deposits derived from local government agencies.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PercentageOfEntityDeposits" xlink:href="fgbi-20251231.xsd#fgbi_PercentageOfEntityDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PercentageOfEntityDeposits" xlink:to="lab_fgbi_PercentageOfEntityDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_019bdcae-e260-7a21-9596-f17e9a427eb1_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_Tier1LeverageRatioIncreaseDecrease_019d2ad6-1d5a-72e9-8a38-d2cdebba23ad_terseLabel_en-US" xlink:label="lab_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in leverage ratio</link:label>
    <link:label id="lab_fgbi_Tier1LeverageRatioIncreaseDecrease_label_en-US" xlink:label="lab_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tier 1 Leverage Ratio, Increase (Decrease)</link:label>
    <link:label id="lab_fgbi_Tier1LeverageRatioIncreaseDecrease_documentation_en-US" xlink:label="lab_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tier 1 Leverage Ratio, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:href="fgbi-20251231.xsd#fgbi_Tier1LeverageRatioIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:to="lab_fgbi_Tier1LeverageRatioIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DoubtfulMember_019bdcae-e261-756f-b326-3322807e133b_terseLabel_en-US" xlink:label="lab_us-gaap_DoubtfulMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Doubtful</link:label>
    <link:label id="lab_us-gaap_DoubtfulMember_label_en-US" xlink:label="lab_us-gaap_DoubtfulMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Doubtful [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DoubtfulMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DoubtfulMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DoubtfulMember" xlink:to="lab_us-gaap_DoubtfulMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019bdcae-e261-7013-a2ea-f0ecc28a9bf2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019bdcae-e261-747f-be88-cedf981bb03c_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount_019bdcae-e2e9-7afa-8bfc-13ae18c1aada_terseLabel_en-US" xlink:label="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded commitments modified during period</link:label>
    <link:label id="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount_label_en-US" xlink:label="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability, Modified In Period, Amount</link:label>
    <link:label id="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount_documentation_en-US" xlink:label="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability, Modified In Period, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:href="fgbi-20251231.xsd#fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:to="lab_fgbi_OffBalanceSheetCreditLossLiabilityModifiedInPeriodAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract_019bdcae-e2e9-7093-8981-2a1b00fc1b60_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held to maturity:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherGeneralExpense_019bdcae-e261-7c6a-9ac7-46957ce2171f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherGeneralExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherGeneralExpense" xlink:to="lab_us-gaap_OtherGeneralExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember_019bdcae-e261-7893-8973-22eec8857e12_terseLabel_en-US" xlink:label="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Government National Mortgage Association (Ginnie Mae-GNMA)</link:label>
    <link:label id="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember_label_en-US" xlink:label="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Government National Mortgage Association (Ginnie Mae-GNMA) [Member]</link:label>
    <link:label id="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember_documentation_en-US" xlink:label="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Government National Mortgage Association (Ginnie Mae-GNMA)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:href="fgbi-20251231.xsd#fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:to="lab_fgbi_GovernmentNationalMortgageAssociationGinnieMaeGNMAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit_019bdcae-e261-7cbe-92f6-21eb180bc25d_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of accounts that exceeded FDIC insurable limit</link:label>
    <link:label id="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit_label_en-US" xlink:label="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Accounts That Exceeded FDIC Insurable Limit</link:label>
    <link:label id="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit_documentation_en-US" xlink:label="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the number of accounts at correspondent banks that exceeded the FDIC insurable limit.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfAccountsThatExceededFDICInsurableLimit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:to="lab_fgbi_NumberOfAccountsThatExceededFDICInsurableLimit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RiskBasedRatiosAbstract_019bdcae-e261-7492-8c22-e71eb78bc9a4_verboseLabel_en-US" xlink:label="lab_us-gaap_RiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Risk-based Capital, Ratio</link:label>
    <link:label id="lab_us-gaap_RiskBasedRatiosAbstract_label_en-US" xlink:label="lab_us-gaap_RiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Risk-Based Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RiskBasedRatiosAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RiskBasedRatiosAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RiskBasedRatiosAbstract" xlink:to="lab_us-gaap_RiskBasedRatiosAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease_019bdcae-e261-7c08-856d-c502917a1b49_terseLabel_en-US" xlink:label="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in available for sale securities</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease_label_en-US" xlink:label="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Period Increase (Decrease)</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:href="fgbi-20251231.xsd#fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:to="lab_fgbi_DebtSecuritiesAvailableForSalePeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019bdcae-e2e9-7ac5-8960-2df6ab62719c_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NumberOfDepositsOfDepositingAuthorities_019bdcae-e261-7b25-a8d0-1df63ad49539_terseLabel_en-US" xlink:label="lab_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of deposits of depositing authorities</link:label>
    <link:label id="lab_fgbi_NumberOfDepositsOfDepositingAuthorities_label_en-US" xlink:label="lab_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of deposits of depositing authorities</link:label>
    <link:label id="lab_fgbi_NumberOfDepositsOfDepositingAuthorities_documentation_en-US" xlink:label="lab_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refer to number of deposits of depositing authorities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfDepositsOfDepositingAuthorities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:to="lab_fgbi_NumberOfDepositsOfDepositingAuthorities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_019bdcae-e261-74a6-a36f-bd6c5c6887f4_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019bdcae-e2e9-750f-bf15-d8a87ec3e261_verboseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Employee Benefit Plans</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket_019bdcae-e2e9-7f41-bf54-e3ce3f633e8d_terseLabel_en-US" xlink:label="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period within which loans are sold in secondary market</link:label>
    <link:label id="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket_label_en-US" xlink:label="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period within Which Loans are Sold in Secondary Market</link:label>
    <link:label id="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket_documentation_en-US" xlink:label="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to the period within which loans held for sale are sold in the secondary market, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:href="fgbi-20251231.xsd#fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:to="lab_fgbi_PeriodWithinWhichLoansAreSoldInSecondaryMarket" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract_019bdcae-e2e9-763a-876e-f73e0affe2d7_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for sale:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities, Continuous Unrealized Loss Position, Qualitative Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionQualitativeDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember_019bdcae-e260-79d9-a44f-0601d3ca22d2_terseLabel_en-US" xlink:label="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Printing Services, Supplies, Office Furniture, and Equipment to Champion Industries, Inc.</link:label>
    <link:label id="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember_label_en-US" xlink:label="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Printing Services, Supplies, Office Furniture, and Equipment to Champion Industries, Inc. [Member]</link:label>
    <link:label id="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember_documentation_en-US" xlink:label="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Printing Services, Supplies, Office Furniture, and Equipment to Champion Industries, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:href="fgbi-20251231.xsd#fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:to="lab_fgbi_PrintingServicesSuppliesOfficeFurnitureAndEquipmentToChampionIndustriesIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_019bdcae-e260-7535-90bd-99f0b8e784b3_periodStartLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unfunded lending commitments, beginning of period</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_019bdcae-e260-7e53-b675-af6dc39d22cc_periodEndLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unfunded lending commitments, end of period</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_019bdcae-e260-7daf-9a88-c5fffbe38267_terseLabel_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses on unfunded lending commitments</link:label>
    <link:label id="lab_us-gaap_OffBalanceSheetCreditLossLiability_label_en-US" xlink:label="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off-Balance-Sheet, Credit Loss, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditLossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditLossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffBalanceSheetCreditLossLiability" xlink:to="lab_us-gaap_OffBalanceSheetCreditLossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019bdcae-e261-7556-affd-a2ee20b5e2a7_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019bdcae-e2e9-71a5-866e-e5319408f391_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_019bdcae-e2e9-782f-a389-4a135a88b7ac_periodStartLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of year</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_019bdcae-e2e9-7417-b7eb-d2b6eefb28c9_periodEndLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of year</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019bdcae-e2e9-7271-8eb5-af2d2a67f1d5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019bdcae-e2e9-7145-bc63-15a20e19cdd4_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019bdcae-e261-713d-915b-f07ce11d584e_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_019bdcae-e2e9-7fbf-aed9-fd34e266cbe1_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward_019bdcae-e2e9-7cec-b0a9-fedee62d672a_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedPartiesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock_019bdcae-e261-777d-936f-665b5106e81d_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale/redemption of Federal Home Loan Bank stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Federal Home Loan Bank Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock" xlink:to="lab_us-gaap_ProceedsFromSaleOfFederalHomeLoanBankStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue_019bdcae-e2e9-78ea-94f1-68bf3bcc5598_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities, available-for-sale and held-to-maturity, fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale and Held-to-Maturity, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019bdcae-e2e9-7f2c-85b6-478afeebcd9e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019bdcae-e261-7ca6-a6a6-c6f351abfd44_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract_019bdcae-e2e9-7ff6-b104-a8a6feadd0bd_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for sale:</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value to Amortized Cost, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesFairValueToAmortizedCostBasisAbstract"/>
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    <link:label id="lab_dei_EntityVoluntaryFilers_019bdcae-e2e9-79ce-b548-01e7b8722e3a_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_MarketableSecuritiesFairValue_019bdcae-e261-77f6-b852-36e4438932fb_terseLabel_en-US" xlink:label="lab_fgbi_MarketableSecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_fgbi_MarketableSecuritiesFairValue_label_en-US" xlink:label="lab_fgbi_MarketableSecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Fair Value</link:label>
    <link:label id="lab_fgbi_MarketableSecuritiesFairValue_documentation_en-US" xlink:label="lab_fgbi_MarketableSecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value of total debt and equity financial instruments including: (1) securities held-to-maturity, (2) trading securities, and (3) securities available-for-sale.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_MarketableSecuritiesFairValue" xlink:href="fgbi-20251231.xsd#fgbi_MarketableSecuritiesFairValue"/>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossAbstract_019bdcae-e261-7dce-ba09-94c3f0b700d3_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss [Abstract]</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossAbstract" xlink:to="lab_us-gaap_AllowanceForCreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount_019bdcae-e261-7bd5-a9e0-0c7a441d7e2b_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through 10 years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 5 through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount"/>
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    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_019bdcae-e2e9-79d4-a0b1-eb6048b960f4_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_label_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Amortization and Accretion, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAmortizationAndAccretionNet"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_019bdcae-e261-7b94-9569-5cef905e2cd0_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premises and equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019bdcae-e2e9-7144-a64d-aa1293706f80_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_Donations_019bdcae-e261-7009-b9f8-3646ab3dfc81_verboseLabel_en-US" xlink:label="lab_fgbi_Donations" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Donations</link:label>
    <link:label id="lab_fgbi_Donations_label_en-US" xlink:label="lab_fgbi_Donations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Donations</link:label>
    <link:label id="lab_fgbi_Donations_documentation_en-US" xlink:label="lab_fgbi_Donations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to donation made during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_Donations" xlink:href="fgbi-20251231.xsd#fgbi_Donations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_Donations" xlink:to="lab_fgbi_Donations" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets_019bdcae-e1a3-7ca2-8d29-895a322ace3f_verboseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Minimum to be Well Capitalized Under Action Provisions</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:to="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract_019bdcae-e261-79d5-a052-dcf8e0a807fd_terseLabel_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Equity Tier One Capital, Ratio</link:label>
    <link:label id="lab_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract_label_en-US" xlink:label="lab_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Equity Tier One Risk Based Ratios [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract" xlink:href="fgbi-20251231.xsd#fgbi_CommonEquityTierOneRiskBasedRatiosAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract" xlink:to="lab_fgbi_CommonEquityTierOneRiskBasedRatiosAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_019bdcae-e261-7ad2-b98f-55308eab53bd_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating Interest Rate Period</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_CreditQualityPolicyTextBlock_019bdcae-e2e9-7405-a32b-56cfff685a72_verboseLabel_en-US" xlink:label="lab_fgbi_CreditQualityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Credit Quality</link:label>
    <link:label id="lab_fgbi_CreditQualityPolicyTextBlock_label_en-US" xlink:label="lab_fgbi_CreditQualityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Quality [Policy Text Block]</link:label>
    <link:label id="lab_fgbi_CreditQualityPolicyTextBlock_documentation_en-US" xlink:label="lab_fgbi_CreditQualityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of accounting policy related to credit quality of loans and lease receivables.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_CreditQualityPolicyTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_CreditQualityPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_CreditQualityPolicyTextBlock" xlink:to="lab_fgbi_CreditQualityPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_019bdcae-e1a3-7a4f-b241-f4f642f999ef_verboseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Less: Provision for credit losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_019bdcae-e1a3-7ec6-904a-8eb0b8044979_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:to="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalFundsSold_019bdcae-e2e9-7d42-ae7a-d93b8fb87790_verboseLabel_en-US" xlink:label="lab_us-gaap_FederalFundsSold" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Federal funds sold</link:label>
    <link:label id="lab_us-gaap_FederalFundsSold_label_en-US" xlink:label="lab_us-gaap_FederalFundsSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Funds Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalFundsSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalFundsSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalFundsSold" xlink:to="lab_us-gaap_FederalFundsSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_019bdcae-e261-75b7-814e-044ef480c4de_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, Number of Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Loss Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepositsAbstract_019bdcae-e260-7ce4-8942-543235e76fe8_verboseLabel_en-US" xlink:label="lab_us-gaap_DepositsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Deposits:</link:label>
    <link:label id="lab_us-gaap_DepositsAbstract_019bdcae-e260-73a0-88d0-2e9d81f9a7db_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits [Abstract]</link:label>
    <link:label id="lab_us-gaap_DepositsAbstract_label_en-US" xlink:label="lab_us-gaap_DepositsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepositsAbstract" xlink:to="lab_us-gaap_DepositsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_019bdcae-e261-74e9-88ee-d6a444f68f4c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Past Due</link:label>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialAssetPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetPastDueMember" xlink:to="lab_us-gaap_FinancialAssetPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract_label_en-US" xlink:label="lab_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Capital Requirements Under Banking Regulations [Abstract]</link:label>
    <link:label id="lab_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract_documentation_en-US" xlink:label="lab_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Regulatory Capital Requirements Under Banking Regulations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract" xlink:href="fgbi-20251231.xsd#fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract" xlink:to="lab_fgbi_RegulatoryCapitalRequirementsUnderBankingRegulationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019bdcae-e261-7bf7-8348-3a84ec2f7cbb_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_019bdcae-e261-773a-9e05-89135165f403_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization/Accretion of investments</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi_019bdcae-e2e9-7514-82fd-bd68c511cc0d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds invested in equity securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equity Securities, FV-NI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireEquitySecuritiesFvNi"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi" xlink:to="lab_us-gaap_PaymentsToAcquireEquitySecuritiesFvNi" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019bdcae-e2e9-7f09-984c-80501721130a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember_019bdcae-e1a3-7b41-a450-01d85c4603d1_terseLabel_en-US" xlink:label="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase And Maintenance Of Automobiles To Hood Automotive Group</link:label>
    <link:label id="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember_label_en-US" xlink:label="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchase And Maintenance Of Automobiles To Hood Automotive Group [Member]</link:label>
    <link:label id="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember_documentation_en-US" xlink:label="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchase And Maintenance Of Automobiles To Hood Automotive Group</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:href="fgbi-20251231.xsd#fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:to="lab_fgbi_PurchaseAndMaintenanceOfAutomobilesToHoodAutomotiveGroupMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_019bdcae-e1a3-7c7f-9d58-634dee3bd17e_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less Than 12 Months, Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, Less than 12 Months, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_019bdcae-e2e9-771f-80b3-000abe9e9c1b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets Subject to Amortization</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing_019bdcae-e261-7e75-b4d2-c6aeb28c1da9_terseLabel_en-US" xlink:label="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension period of majority of short-term borrowing</link:label>
    <link:label id="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing_label_en-US" xlink:label="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extension Period of majority of Short Term Borrowing</link:label>
    <link:label id="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing_documentation_en-US" xlink:label="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to extension period of majority of short term borrowings of the entity, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:href="fgbi-20251231.xsd#fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:to="lab_fgbi_ExtensionPeriodOfMajorityOfShortTermBorrowing" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ConstructionAndLandDevelopmentMember_019bdcae-e261-7f36-a8d1-668be6e788c6_verboseLabel_en-US" xlink:label="lab_fgbi_ConstructionAndLandDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Construction &amp; land development</link:label>
    <link:label id="lab_fgbi_ConstructionAndLandDevelopmentMember_019bdcae-e261-7ba2-affa-a91742b78ccb_terseLabel_en-US" xlink:label="lab_fgbi_ConstructionAndLandDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction &amp; land development</link:label>
    <link:label id="lab_fgbi_ConstructionAndLandDevelopmentMember_label_en-US" xlink:label="lab_fgbi_ConstructionAndLandDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction and Land Development [Member]</link:label>
    <link:label id="lab_fgbi_ConstructionAndLandDevelopmentMember_documentation_en-US" xlink:label="lab_fgbi_ConstructionAndLandDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the construction of real property or the development of land.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ConstructionAndLandDevelopmentMember" xlink:href="fgbi-20251231.xsd#fgbi_ConstructionAndLandDevelopmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ConstructionAndLandDevelopmentMember" xlink:to="lab_fgbi_ConstructionAndLandDevelopmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_019bdcae-e261-772a-9035-f05e768627e6_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Investment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:to="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions_019bdcae-e1a3-71bc-9557-7c79f7dd9dc4_terseLabel_en-US" xlink:label="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net costs from other real estate and repossessions</link:label>
    <link:label id="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions_label_en-US" xlink:label="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net costs from other real estate and repossessions</link:label>
    <link:label id="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions_documentation_en-US" xlink:label="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to non interest net costs from other real estate and repossessions during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:href="fgbi-20251231.xsd#fgbi_NetCostsFromOtherRealEstateAndRepossessions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:to="lab_fgbi_NetCostsFromOtherRealEstateAndRepossessions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AutomatedTellerMachineFees_019bdcae-e260-78ec-9667-2b77d6d63183_verboseLabel_en-US" xlink:label="lab_fgbi_AutomatedTellerMachineFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">ATM Fees</link:label>
    <link:label id="lab_fgbi_AutomatedTellerMachineFees_label_en-US" xlink:label="lab_fgbi_AutomatedTellerMachineFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Automated Teller Machine Fees</link:label>
    <link:label id="lab_fgbi_AutomatedTellerMachineFees_documentation_en-US" xlink:label="lab_fgbi_AutomatedTellerMachineFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount of fees charged for the use of automated teller machines (ATM) during the period.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AutomatedTellerMachineFees" xlink:href="fgbi-20251231.xsd#fgbi_AutomatedTellerMachineFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AutomatedTellerMachineFees" xlink:to="lab_fgbi_AutomatedTellerMachineFees" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind_019c7ac5-9897-741d-9cca-7d99040f776e_terseLabel_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock issued in payment-in-kind (in shares)</link:label>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind_label_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Issued As Payment-In-Kind</link:label>
    <link:label id="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind_documentation_en-US" xlink:label="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Issued As Payment-In-Kind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:href="fgbi-20251231.xsd#fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:to="lab_fgbi_StockIssuedDuringPeriodSharesIssuedAsPaymentInKind" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1_019c562b-4374-76e8-a69a-b0fadac71401_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans that were modified with in the previous 12 months</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Modified, Subsequent Default</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:to="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019bdcae-e260-750d-b8f1-7dd533984a5b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepositsMember_019bdcae-e1a3-7f7c-b9c3-ab3db6a92887_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_us-gaap_DepositsMember_label_en-US" xlink:label="lab_us-gaap_DepositsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepositsMember" xlink:to="lab_us-gaap_DepositsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019bdcae-e2e9-7783-ad60-3d6511b94300_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_019bdcae-e260-7ead-97a7-e2d6d74097db_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock $1,000 Par</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment_019bdcae-e261-7cf6-b75c-2914bc678bf1_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans Collectively Evaluated</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Collectively Evaluated for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment" xlink:to="lab_us-gaap_FinancingReceivableCollectivelyEvaluatedForImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount_019bdcae-e260-7056-b005-f0e3141ba9f4_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year One through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount"/>
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    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_019bdcae-e1a3-75df-bef0-1396a2a80ed6_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_IcfrAuditorAttestationFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_IcfrAuditorAttestationFlag"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_019bdcae-e260-7d32-b308-4b46565f8b8d_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employer matching contribution</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:to="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_019c7b39-acec-7f52-9843-eb381a70dde6_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common Stock issued in subordinated debt conversion</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears_019bdcae-e260-736b-ac75-249b16f2a0ea_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One to five years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears_label_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing receivables that are maturing after one year but not more than five years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing receivables, excluding nonaccrual status notes, gross carrying amount that are maturing after one year but not more than five years.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:to="lab_fgbi_FinancingReceivablesThatAreMaturingAfterOneYearButNotMoreThanFiveYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanDisclosureLineItems_019bdcae-e2e9-75fe-b874-a6bdb93acee4_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan Disclosure [Line Items]</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanDisclosureLineItems_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanDisclosureLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanDisclosureLineItems" xlink:to="lab_us-gaap_DefinedContributionPlanDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfCondensedIncomeStatementTableTextBlock_019bdcae-e2e9-7b88-a2cb-6c0cc9dfec43_verboseLabel_en-US" xlink:label="lab_srt_ScheduleOfCondensedIncomeStatementTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Condensed Statements of Income</link:label>
    <link:label id="lab_srt_ScheduleOfCondensedIncomeStatementTableTextBlock_label_en-US" xlink:label="lab_srt_ScheduleOfCondensedIncomeStatementTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Condensed Income Statement [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfCondensedIncomeStatementTableTextBlock" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfCondensedIncomeStatementTableTextBlock"/>
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    <link:label id="lab_dei_AuditorFirmId_019bdcae-e1a3-7232-9e04-a3ef87d42e46_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:label id="lab_dei_AuditorFirmId_label_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorFirmId" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorFirmId"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorFirmId" xlink:to="lab_dei_AuditorFirmId" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_019bdcae-e2e9-7822-a1dd-8b3b3c9e0bdc_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available lines of credit including FHLB</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember_019bdcae-e2e9-7617-905e-570f8837333f_terseLabel_en-US" xlink:label="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single-Family Residential</link:label>
    <link:label id="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember_label_en-US" xlink:label="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single Family Residential Real Estate Loan [Member]</link:label>
    <link:label id="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember_documentation_en-US" xlink:label="lab_fgbi_SingleFamilyResidentialRealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the purchase of single family residential real property.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SingleFamilyResidentialRealEstateLoanMember" xlink:href="fgbi-20251231.xsd#fgbi_SingleFamilyResidentialRealEstateLoanMember"/>
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    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_019bdcae-e261-76a4-a0d9-ab83abcf6635_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019bdcae-e1a3-73dc-9f37-c362dee1ec2f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
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    <link:label id="lab_fgbi_TimeDeposits250000OrMore_019bdcae-e2e9-7cfb-aeaa-f725b78811c6_terseLabel_en-US" xlink:label="lab_fgbi_TimeDeposits250000OrMore" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate amount of time deposits in denominations of $250,000 or more</link:label>
    <link:label id="lab_fgbi_TimeDeposits250000OrMore_label_en-US" xlink:label="lab_fgbi_TimeDeposits250000OrMore" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposits $250,000 Or More</link:label>
    <link:label id="lab_fgbi_TimeDeposits250000OrMore_documentation_en-US" xlink:label="lab_fgbi_TimeDeposits250000OrMore" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Time Deposits $250,000 Or More</link:label>
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    <link:label id="lab_us-gaap_LinesOfCreditCurrent_019bdcae-e2e9-7a9b-a6b3-a9cc515b7ae8_terseLabel_en-US" xlink:label="lab_us-gaap_LinesOfCreditCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit</link:label>
    <link:label id="lab_us-gaap_LinesOfCreditCurrent_label_en-US" xlink:label="lab_us-gaap_LinesOfCreditCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LinesOfCreditCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LinesOfCreditCurrent"/>
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    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019d44a6-f283-70cb-99f5-845ecec17317_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
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    <link:label id="lab_us-gaap_InterestExpenseAbstract_019bdcae-e1a3-7107-8314-40645a3d81cb_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense:</link:label>
    <link:label id="lab_us-gaap_InterestExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_InterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseAbstract" xlink:to="lab_us-gaap_InterestExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_019bdcae-e260-73a3-aa0c-d4b4763505aa_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
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    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_019bdcae-e261-7ce2-8347-8f91b0f0d0f1_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per common share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_019bdcae-e2e9-7a8b-bf0a-96af017b687a_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Real Estate</link:label>
    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOwnedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateOwnedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOwnedTextBlock" xlink:to="lab_us-gaap_RealEstateOwnedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_Multi-FamilyMember_019bdcae-e2e9-71d1-9ef1-98dce6716af1_terseLabel_en-US" xlink:label="lab_fgbi_Multi-FamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multifamily</link:label>
    <link:label id="lab_fgbi_Multi-FamilyMember_019bdcae-e2e9-75f3-a3a4-7aa8809c0768_verboseLabel_en-US" xlink:label="lab_fgbi_Multi-FamilyMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Multifamily</link:label>
    <link:label id="lab_fgbi_Multi-FamilyMember_label_en-US" xlink:label="lab_fgbi_Multi-FamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family [Member]</link:label>
    <link:label id="lab_fgbi_Multi-FamilyMember_documentation_en-US" xlink:label="lab_fgbi_Multi-FamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan to finance the purchase of multi-family residential real property.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_Multi-FamilyMember" xlink:href="fgbi-20251231.xsd#fgbi_Multi-FamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_Multi-FamilyMember" xlink:to="lab_fgbi_Multi-FamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_019bdcae-e261-7ee1-9b3e-c93a2332df34_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_019bdcae-e261-71a1-92e2-5b2739835790_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds invested in AFS securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLossAbstract_019bdcae-e261-745c-9c93-4f6be0a563f4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Income</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLossAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLossAbstract" xlink:to="lab_us-gaap_OperatingIncomeLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_019bdcae-e261-71fa-898e-37301c538694_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cumulative perpetual; 34,500 shares issued and outstanding, respectively</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_019bdcae-e1a3-76d1-b1ff-36afc9430b5d_terseLabel_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Municipal bonds</link:label>
    <link:label id="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember_label_en-US" xlink:label="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US States and Political Subdivisions Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USStatesAndPoliticalSubdivisionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:to="lab_us-gaap_USStatesAndPoliticalSubdivisionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock_019bdcae-e261-78ce-acc1-65eb69a93409_terseLabel_en-US" xlink:label="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Comparison of Securities by Type</link:label>
    <link:label id="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock_label_en-US" xlink:label="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Held-to-maturity Securities Reconciliation [Table Text Block]</link:label>
    <link:label id="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock_documentation_en-US" xlink:label="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of the reconciliation of available-for-sale and held-to-maturity securities from cost basis to fair value.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:href="fgbi-20251231.xsd#fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:to="lab_fgbi_ScheduleOfAvailableForSaleAndHeldToMaturitySecuritiesReconciliationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanTable_019bdcae-e2e9-715e-8d89-43282b82b5ab_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan [Table]</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanTable_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanTable" xlink:to="lab_us-gaap_DefinedContributionPlanTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019bdcae-e261-7304-9bff-3c5c939c5532_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_019bdcae-e261-78bb-8af0-578745469dbc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated, year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_019bdcae-e2e9-71c6-84ec-8407199b2762_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated Debt</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebtMember" xlink:to="lab_us-gaap_SubordinatedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019bdcae-e2e9-7dd2-8a6b-0093949a49bc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_019bdcae-e2e9-7228-988d-2545beaef68c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Deferred Taxes</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncome_019bdcae-e2e9-7494-9d12-27d4ab6df256_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncome_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherOperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncome" xlink:to="lab_us-gaap_OtherOperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019bdcae-e261-79ac-9bd5-11c633abc54f_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $1 par value - 100,600,000 shares authorized; 15,793,433 and 12,504,717 shares issued and outstanding</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDepositsByMaturityAbstract_019bdcae-e260-7ac2-ae02-298fb28d99c4_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositsByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maturities of time deposits</link:label>
    <link:label id="lab_us-gaap_TimeDepositsByMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_TimeDepositsByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposits, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositsByMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositsByMaturityAbstract"/>
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    <link:label id="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued_019bdcae-e2e9-76f9-bf7c-87472e1587bb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExaminationPenaltiesAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax examination, penalties accrued</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff_019bdcae-e1a3-74a4-bc0b-fda47af91f9d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated write off, year one</link:label>
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    <link:label id="lab_us-gaap_MarketableSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019bdcae-e261-7b5d-957d-fd371549b78f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
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    <link:label id="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount_label_en-US" xlink:label="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans in Process of Foreclosure, Amount</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_019bdcae-e2e9-7600-bf77-fba89fcefae5_verboseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_019bdcae-e261-7d76-93df-ec28b033cae1_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
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    <link:label id="lab_fgbi_FederalHomeLoanMortgageCorporationFreddieMacFHLMCMember_019bdcae-e2e9-7eaa-a084-e343f21579a0_terseLabel_en-US" xlink:label="lab_fgbi_FederalHomeLoanMortgageCorporationFreddieMacFHLMCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal Home Loan Mortgage Corporation (Freddie Mac-FHLMC)</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019bdcae-e261-70f6-b8d7-fca3d07bad6b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 10 years</link:label>
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    <link:label id="lab_fgbi_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIncludingOffBalanceSheetCreditLossLiability_019bdcae-e261-7f84-8284-7f01d0850f53_periodStartLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIncludingOffBalanceSheetCreditLossLiability" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Total, beginning balance</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DeferredTaxAssetDebtSecuritiesAvailableForSaleSecuritiesTransferredToHeldToMaturityUnrealizedLoss" xlink:to="lab_fgbi_DeferredTaxAssetDebtSecuritiesAvailableForSaleSecuritiesTransferredToHeldToMaturityUnrealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract_019bdcae-e2e9-7e98-a79c-9d4822ce0dd8_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents:</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_019bdcae-e1a3-78ec-a8ec-aa6c6de99ae7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_019cf688-6271-7bc8-89a0-ee1c62f0533b_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of common stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet_019bdcae-e261-790e-8a6a-e00a331f7d28_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers in and/or out of Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_019bdcae-e261-7555-93e6-3ca02e3ce7b1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross realized losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage_019bdcae-e2e9-7363-8b80-8006e77ff291_terseLabel_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum employer matching contribution percentage</link:label>
    <link:label id="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage_label_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Maximum Matching Percentage</link:label>
    <link:label id="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage_documentation_en-US" xlink:label="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to maximum percentage up to which employer matching contribution may be matched.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:href="fgbi-20251231.xsd#fgbi_DefinedContributionPlanMaximumMatchingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:to="lab_fgbi_DefinedContributionPlanMaximumMatchingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019bdcae-e2e9-79a7-87d8-900dd312b060_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResidentialRealEstateMember_019bdcae-e261-76f3-98e9-6820e46454fd_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential</link:label>
    <link:label id="lab_us-gaap_ResidentialRealEstateMember_label_en-US" xlink:label="lab_us-gaap_ResidentialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Real Estate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialRealEstateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResidentialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResidentialRealEstateMember" xlink:to="lab_us-gaap_ResidentialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_019bdcae-e261-7e0c-9ee5-22f1f945c942_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019bdcae-e2e9-73e4-a74c-c50bc592c1cb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of premises and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy_019bdcae-e261-7af2-b1f2-723ca88ca634_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other real estate</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Real Estate Acquired Through Foreclosure [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRealEstateAcquiredThroughForeclosurePolicy"/>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_019d308d-a9c0-7bcb-8fed-430d0c093165_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment_019bdcae-e2e9-76b1-9653-6c3a7197fd0f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans Individually Evaluated</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Individually Evaluated for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment" xlink:to="lab_us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_019bdcae-e261-7c0b-909f-98b08624b541_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated write off, year five</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Five, Originated, Four Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019bdcae-e2e9-7756-823a-391c18442071_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract_019bdcae-e2e9-7740-b3a0-50b1817614b1_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivables, Fixed and Floating Rate Loans by Contractual Maturity [Abstract]</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract_label_en-US" xlink:label="lab_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivables, Fixed and Floating Rate Loans by Contractual Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract" xlink:to="lab_fgbi_FinancingReceivablesFixedAndFloatingRateLoansByContractualMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_019d2ad6-1d5a-7465-9558-b34034690f72_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss_019bdcae-e261-7238-be38-9692d9d8d4cb_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total, Gross Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_019bdcae-e261-7a83-8e83-f0835e28aa47_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_019cb287-c893-75aa-a5d9-8eba706fb818_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Newly issued common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_label_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember_019bdcae-e1a3-7e58-95b0-565d61f468e9_terseLabel_en-US" xlink:label="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-Maturity and Available-for-Sale Securities</link:label>
    <link:label id="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember_label_en-US" xlink:label="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-to-Maturity and Available-for-Sale Securities [Member]</link:label>
    <link:label id="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember_documentation_en-US" xlink:label="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity and Available-for-Sale Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:href="fgbi-20251231.xsd#fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:to="lab_fgbi_HeldToMaturityAndAvailableForSaleSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_019bdcae-e2e9-72cd-a49c-6a78b841112d_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in other assets and liabilities, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedRateResidentialMortgageMember_019bdcae-e2e9-7303-8fa9-e06a8e950abb_terseLabel_en-US" xlink:label="lab_us-gaap_FixedRateResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Rate Residential Mortgage</link:label>
    <link:label id="lab_us-gaap_FixedRateResidentialMortgageMember_label_en-US" xlink:label="lab_us-gaap_FixedRateResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate Residential Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedRateResidentialMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedRateResidentialMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedRateResidentialMortgageMember" xlink:to="lab_us-gaap_FixedRateResidentialMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment_019bdcae-e261-7517-a690-ff84e16777c6_terseLabel_en-US" xlink:label="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual payment due</link:label>
    <link:label id="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment_label_en-US" xlink:label="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Annual Payment</link:label>
    <link:label id="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment_documentation_en-US" xlink:label="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Annual Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:href="fgbi-20251231.xsd#fgbi_LesseeOperatingLeaseLiabilityAnnualPayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:to="lab_fgbi_LesseeOperatingLeaseLiabilityAnnualPayment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019bdcae-e1a3-7eb1-be0f-bfc7193088a0_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019bdcae-e261-7ea0-a2d6-33d78bbbb6c5_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_019bdcae-e2e9-7a3c-ae23-4b78390781e2_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019bdcae-e261-7339-a29d-f774621692ce_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_019bdcae-e2e9-708d-a6ff-5de7552679a7_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract"/>
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    <link:label id="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus_019bdcae-e260-7ba9-ab3f-9e1005aa8e4e_terseLabel_en-US" xlink:label="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period of payment performance after which loans are returned to accrual status</link:label>
    <link:label id="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus_label_en-US" xlink:label="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period of Payment Performance After Which Loans are Returned to Accrual Status</link:label>
    <link:label id="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus_documentation_en-US" xlink:label="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period of payment performance after which loans are returned to accrual status, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:href="fgbi-20251231.xsd#fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:to="lab_fgbi_PeriodOfPaymentPerformanceAfterWhichLoansAreReturnedToAccrualStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaidInKindInterest_019c7b9f-9d36-73ce-83d6-2eee25058d94_terseLabel_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense paid-in-kind</link:label>
    <link:label id="lab_us-gaap_PaidInKindInterest_label_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paid-in-Kind Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaidInKindInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaidInKindInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaidInKindInterest" xlink:to="lab_us-gaap_PaidInKindInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019bdcae-e2e9-72ec-b096-286e13507957_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Per Common Share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_019bdcae-e2e9-72dd-bcf0-f27eb9ede137_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears_019bdcae-e1a3-7362-b1e3-d0cf8e96c56c_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 15 years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears_label_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing receivables that are maturing after fifteen years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing receivables, excluding nonaccrual status notes, gross carrying amount that are maturing after fifteen years.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:to="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFifteenYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_019bdcae-e260-7565-a685-e9b8674e3240_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated write off, year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FurnitureAndEquipmentMember_019bdcae-e261-75f6-b12c-1ed81d94b2dd_terseLabel_en-US" xlink:label="lab_fgbi_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and equipment</link:label>
    <link:label id="lab_fgbi_FurnitureAndEquipmentMember_label_en-US" xlink:label="lab_fgbi_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Equipment [Member]</link:label>
    <link:label id="lab_fgbi_FurnitureAndEquipmentMember_documentation_en-US" xlink:label="lab_fgbi_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment commonly used in offices and stores that have no permanent connection to the structure of a building or utilities and tangible personal property used to produce goods and services.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FurnitureAndEquipmentMember" xlink:href="fgbi-20251231.xsd#fgbi_FurnitureAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FurnitureAndEquipmentMember" xlink:to="lab_fgbi_FurnitureAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_019bdcae-e260-7109-b81f-1caf67e9234a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_019bdcae-e1a3-7dc1-b766-5f79ff130d47_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Loaned or Sold under Agreements to Repurchase, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:to="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss_019cf6f3-5b1a-7720-9d55-d2055d8c397c_terseLabel_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securities with impairment loss</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss_label_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity, Number Of Securities With Impairment Loss</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-To-Maturity, Number Of Securities With Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:href="fgbi-20251231.xsd#fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:to="lab_fgbi_DebtSecuritiesHeldToMaturityNumberOfSecuritiesWithImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree_019bdcae-e2e9-753e-8c8b-b8cb3dd374cd_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial fixed rate period, tranche three</link:label>
    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree_label_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Initial Fixed Rate Period, Tranche Three</link:label>
    <link:label id="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Initial Fixed Rate Period, Tranche Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:to="lab_fgbi_FinancingReceivableInitialFixedRatePeriodTrancheThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_019bdcae-e261-751c-a603-8e8e3de68047_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_019cf69f-7d97-7431-97bd-86204b33d13a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_019bdcae-e2e9-703b-8aa2-f2db6634052a_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoanRestructuringModificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanRestructuringModificationDomain" xlink:to="lab_us-gaap_LoanRestructuringModificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019bdcae-e2e9-711c-8dc7-3f9aa35015fe_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019bdcae-e2e9-77cc-b0b9-4c63e77b60df_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019bdcae-e2e9-7b89-9d8d-cb33f3d1b78a_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (Loss) Income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019bdcae-e2e9-7db1-83d6-0387200c6c51_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (Loss) Income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019c7b60-5a22-7442-9200-e323f5cd97ef_netLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019bdcae-e2e9-7670-899f-0a9ea08b4981_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_019bdcae-e1a3-73a3-9ee6-e3df3e47700f_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable"/>
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    <link:label id="lab_us-gaap_CapitalToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalToRiskWeightedAssets"/>
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    <link:label id="lab_us-gaap_ConstructionInProgressMember_019bdcae-e2e9-723f-a037-560a74073c68_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in progress</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressMember" xlink:to="lab_us-gaap_ConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_019bdcae-e261-719c-b4c9-2b66f67630f0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Statutory Federal Income Tax Rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_019d0b4e-9e69-734a-a678-74fdcec5d3e1_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
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    <link:label id="lab_fgbi_AccruedInterestReceivableFairValueDisclosure_019bdcae-e2e9-7b51-bf9f-28bace0e6ffc_terseLabel_en-US" xlink:label="lab_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_fgbi_AccruedInterestReceivableFairValueDisclosure_label_en-US" xlink:label="lab_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Interest Receivable, Fair Value Disclosure</link:label>
    <link:label id="lab_fgbi_AccruedInterestReceivableFairValueDisclosure_documentation_en-US" xlink:label="lab_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Interest Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:href="fgbi-20251231.xsd#fgbi_AccruedInterestReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:to="lab_fgbi_AccruedInterestReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019bdcae-e261-733c-b874-fc7ec17be6d6_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized"/>
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    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears_019bdcae-e1a3-7c57-a1a1-a2c7c1650b89_terseLabel_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Five to 15 years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears_label_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing receivables that are maturing after five years but not more than fifteen years</link:label>
    <link:label id="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears_documentation_en-US" xlink:label="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing receivables, excluding nonaccrual status notes, gross carrying amount that are maturing after five years but not more than fifteen years.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:href="fgbi-20251231.xsd#fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:to="lab_fgbi_FinancingReceivablesThatAreMaturingAfterFiveYearsButNotMoreThanFifteenYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_019bdcae-e261-78ff-a58f-ecaf12765054_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_019bdcae-e2e9-7a9a-93e0-56ef5a322f20_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, operating lease, term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019d0b49-2d28-7afb-99ec-6c255153de37_negatedLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net operating loss</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019bdcae-e261-7d1b-ae76-d6ec7c75cb2f_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
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    <link:label id="lab_fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract_019bdcae-e2e9-792d-89cd-db0d78e010b4_verboseLabel_en-US" xlink:label="lab_fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of certain information short-term borrowings [Abstract]</link:label>
    <link:label id="lab_fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract_label_en-US" xlink:label="lab_fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Certain Information Short term Borrowings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract" xlink:href="fgbi-20251231.xsd#fgbi_ScheduleOfCertainInformationShortTermBorrowingsAbstract"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans_019c7bb3-fe61-7d2c-855d-126a76fc98e9_terseLabel_en-US" xlink:label="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of real estate in settlement of loans</link:label>
    <link:label id="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans_label_en-US" xlink:label="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition Of Real Estate In Settlement Of Loans</link:label>
    <link:label id="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans_documentation_en-US" xlink:label="lab_fgbi_AcquisitionOfRealEstateInSettlementOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Of Real Estate In Settlement Of Loans</link:label>
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    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions_019bdcae-e260-76b7-a82d-31c28c183da6_terseLabel_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of debt securities with unrealized losses</link:label>
    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions_label_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:label id="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions_documentation_en-US" xlink:label="lab_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of debt securities in a continuous debt positions of unrealized loss for which an other-than-temporary impairment (OTTI) has not been recognized in the income statement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions" xlink:href="fgbi-20251231.xsd#fgbi_SecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositions"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities_019cc1a9-4f8c-7c4e-a3d7-0fb29b45bccb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds invested in HTM securities</link:label>
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    <link:label id="lab_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract_019bdcae-e261-7fd6-800a-c2d53da627ba_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned Acquired by Foreclosure:</link:label>
    <link:label id="lab_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate, Foreclosed Assets, and Repossessed Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherRealEstateAndForeclosedAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract" xlink:to="lab_us-gaap_OtherRealEstateAndForeclosedAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions_019bdcae-e2e9-7bb0-bf13-cfad7c8587a6_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less Than 12 Months, Number of Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions"/>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019bdcae-e260-7714-bcc1-6a56ae212e64_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019bdcae-e1a3-78d9-a5eb-a566aea42780_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum_019bdcae-e1a3-7e70-a310-1b403dcfef8d_terseLabel_en-US" xlink:label="lab_us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital conservation buffer minimum</link:label>
    <link:label id="lab_us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum_label_en-US" xlink:label="lab_us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Capital Conservation Buffer, Capital Conserved, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankingRegulationCapitalConservationBufferCapitalConservedMinimum"/>
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    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_019bdcae-e2e9-7ba8-9f29-249252bab96c_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019bdcae-e2e9-793d-881d-af8b035e7f79_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AmortizationOfCoreDeposits_019bdcae-e2e9-78ac-9341-920b3c2649e4_terseLabel_en-US" xlink:label="lab_fgbi_AmortizationOfCoreDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of core deposits</link:label>
    <link:label id="lab_fgbi_AmortizationOfCoreDeposits_label_en-US" xlink:label="lab_fgbi_AmortizationOfCoreDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of core deposits</link:label>
    <link:label id="lab_fgbi_AmortizationOfCoreDeposits_documentation_en-US" xlink:label="lab_fgbi_AmortizationOfCoreDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to amortization of entity's long-term relationships with depositors, commonly known as core deposit intangibles, which are separate from the financial instruments themselves.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AmortizationOfCoreDeposits" xlink:href="fgbi-20251231.xsd#fgbi_AmortizationOfCoreDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AmortizationOfCoreDeposits" xlink:to="lab_fgbi_AmortizationOfCoreDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019cf6a1-c771-72f2-9d49-d1ca2063089b_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Deferred</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019bdcae-e261-782b-8055-cf5583c5a02e_verboseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net (loss) income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019bdcae-e261-7943-ad72-30e9260bd59d_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019bdcae-e2e9-773d-8f6b-810fd6720bb8_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows From Financing Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019bdcae-e2e9-7729-823e-b967af537e8f_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_019bdcae-e261-7f39-891a-a13e0550c86f_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
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    <link:label id="lab_us-gaap_GainsLossesOnSalesOfAssets_019bdcae-e2e9-740a-bfb0-15a6992b9981_negatedLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Loss (gain) on sale of assets</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfAssets_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Assets for Financial Service Operations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnSalesOfAssets"/>
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    <link:label id="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1_019bdcae-e261-7d4a-bddd-c299067232c5_terseLabel_en-US" xlink:label="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ATM and debit card fees</link:label>
    <link:label id="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1_label_en-US" xlink:label="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fees And Commissions Credit And Debit Cards 1</link:label>
    <link:label id="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1_documentation_en-US" xlink:label="lab_fgbi_FeesAndCommissionsCreditAndDebitCards1" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fees And Commissions Credit And Debit Cards 1</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019bdcae-e2e9-707c-8135-612991c1344d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unobservable Input Reconciliation</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019bdcae-e2e9-7384-b936-80e12b4fd977_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019bdcae-e2e9-71d8-8c7b-f96827210e49_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: allowance for credit losses</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019bdcae-e2e9-7082-89c8-dd7a530cce53_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Allowance for Credit Losses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
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    <link:label id="lab_us-gaap_ReceivableTypeDomain_019bdcae-e261-7461-baae-518a2ccf08ea_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_srt_DirectorMember_019bdcae-e1a3-7fc4-8b13-9711b74e0699_terseLabel_en-US" xlink:label="lab_srt_DirectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Director</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019bdcae-e2e9-79fc-b373-20b966de0f86_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
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    <link:label id="lab_fgbi_DebtSecuritiesAccruedInterest_label_en-US" xlink:label="lab_fgbi_DebtSecuritiesAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Accrued Interest</link:label>
    <link:label id="lab_fgbi_DebtSecuritiesAccruedInterest_documentation_en-US" xlink:label="lab_fgbi_DebtSecuritiesAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_DebtSecuritiesAccruedInterest" xlink:href="fgbi-20251231.xsd#fgbi_DebtSecuritiesAccruedInterest"/>
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    <link:label id="lab_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue_label_en-US" xlink:label="lab_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Consecutive Payments Missed after Which Loans are Considered Past Due</link:label>
    <link:label id="lab_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue_documentation_en-US" xlink:label="lab_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to the number of consecutive payments missed, after which loans are considered past due.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue" xlink:href="fgbi-20251231.xsd#fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue" xlink:to="lab_fgbi_NumberOfConsecutivePaymentsMissedAfterWhichLoansAreConsideredPastDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_019bdcae-e2e9-7d76-be65-dc0236fcab41_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized holding gains arising during the period</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019bdcae-e2e9-78d1-b47b-a0261ad18141_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019bdcae-e261-7d26-88ba-a46df9f77719_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_AuditInformationAbstract_label_en-US" xlink:label="lab_fgbi_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Audit Information [Abstract]</link:label>
    <link:label id="lab_fgbi_AuditInformationAbstract_documentation_en-US" xlink:label="lab_fgbi_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Audit Information</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_AuditInformationAbstract" xlink:href="fgbi-20251231.xsd#fgbi_AuditInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_AuditInformationAbstract" xlink:to="lab_fgbi_AuditInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_019bdcae-e2e9-7f12-9cd1-6cc57f7f11d3_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and Due from Banks</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_019bdcae-e2e9-7a6c-849d-b0da481bdfe0_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gains on sale of equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_019cf68e-d10e-7c36-85e2-d37d2ce3c11a_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment charge</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfRealEstate" xlink:to="lab_us-gaap_ImpairmentOfRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_019d308e-fce5-7710-a938-a829b5bac695_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal group, loans</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accounts, Notes and Loans Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsNotesAndLoansReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019bdcae-e2e9-758d-b900-92425fb6c1ea_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_019bdcae-e2e9-79b7-9429-93b93b666881_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Dividends paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Capital_019bdcae-e2e9-732a-974f-be8271788d9b_verboseLabel_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Actual</link:label>
    <link:label id="lab_us-gaap_Capital_label_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Capital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Capital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Capital" xlink:to="lab_us-gaap_Capital" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember_019bdcae-e260-7bb2-981a-09fe82098810_terseLabel_en-US" xlink:label="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Subordinated Debt Instrument One</link:label>
    <link:label id="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember_label_en-US" xlink:label="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Debt Instrument One [Member]</link:label>
    <link:label id="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember_documentation_en-US" xlink:label="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Debt Instrument One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:href="fgbi-20251231.xsd#fgbi_JuniorSubordinatedDebtInstrumentOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:to="lab_fgbi_JuniorSubordinatedDebtInstrumentOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OccupancyNet_019bdcae-e2e9-7788-be07-7c4321b6cf84_terseLabel_en-US" xlink:label="lab_us-gaap_OccupancyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Occupancy and equipment expense</link:label>
    <link:label id="lab_us-gaap_OccupancyNet_label_en-US" xlink:label="lab_us-gaap_OccupancyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Occupancy, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OccupancyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OccupancyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OccupancyNet" xlink:to="lab_us-gaap_OccupancyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019bdcae-e2e9-7e50-817a-d82e5749c682_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_019bdcae-e2e9-7351-9841-1d9559c24f7a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_EquipmentFixturesAndAutomobilesMember_019bdcae-e261-752e-8fe6-5cc27f32c5de_terseLabel_en-US" xlink:label="lab_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment, Fixtures and Automobiles</link:label>
    <link:label id="lab_fgbi_EquipmentFixturesAndAutomobilesMember_label_en-US" xlink:label="lab_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment, fixtures and automobiles [Member]</link:label>
    <link:label id="lab_fgbi_EquipmentFixturesAndAutomobilesMember_documentation_en-US" xlink:label="lab_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Vehicles that are used primarily for transporting people. Equipment commonly used in offices and stores that have no permanent connection to the structure of a building or utilities. Examples include, but are not limited to, desks, chairs, tables, and bookcases.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:href="fgbi-20251231.xsd#fgbi_EquipmentFixturesAndAutomobilesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:to="lab_fgbi_EquipmentFixturesAndAutomobilesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_019bdcae-e2e9-700c-87d7-827c575420b6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAxis_019bdcae-e261-7621-b6f1-8dac8c747073_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Axis]</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAxis_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAxis" xlink:to="lab_us-gaap_CashAndCashEquivalentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_019bdcae-e2e9-704b-ad67-988cacb50f46_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Subtotal</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
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    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities_019bdcae-e2e9-719a-804a-bb281fa80f77_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from maturities, calls and sales of AFS securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:to="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
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    <link:label id="lab_us-gaap_DepositsSavingsDeposits_019bdcae-e2e9-7ff3-8e9a-7c47dcfb924c_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings</link:label>
    <link:label id="lab_us-gaap_DepositsSavingsDeposits_label_en-US" xlink:label="lab_us-gaap_DepositsSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits, Savings Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositsSavingsDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsSavingsDeposits"/>
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    <link:label id="lab_us-gaap_OtherRealEstateAndForeclosedAssets_019bdcae-e261-7299-94a6-6b78bb3609d1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherRealEstateAndForeclosedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other real estate, net</link:label>
    <link:label id="lab_us-gaap_OtherRealEstateAndForeclosedAssets_019bdcae-e261-745f-9b03-33e94914bd98_totalLabel_en-US" xlink:label="lab_us-gaap_OtherRealEstateAndForeclosedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Other Real Estate Owned and Foreclosed Property</link:label>
    <link:label id="lab_us-gaap_OtherRealEstateAndForeclosedAssets_label_en-US" xlink:label="lab_us-gaap_OtherRealEstateAndForeclosedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate, Foreclosed Assets, and Repossessed Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherRealEstateAndForeclosedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherRealEstateAndForeclosedAssets"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019bdcae-e261-79c0-8625-d2bf362979fc_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019bdcae-e261-7c79-80e9-da08437d3229_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock issued</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_fgbi_ConsumerAndOtherMember_019bdcae-e261-7731-829a-bf17762cf68f_terseLabel_en-US" xlink:label="lab_fgbi_ConsumerAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other</link:label>
    <link:label id="lab_fgbi_ConsumerAndOtherMember_019bdcae-e261-7c92-a5e8-d6d8fe5a1e7a_verboseLabel_en-US" xlink:label="lab_fgbi_ConsumerAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other loans</link:label>
    <link:label id="lab_fgbi_ConsumerAndOtherMember_label_en-US" xlink:label="lab_fgbi_ConsumerAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer and Other [Member]</link:label>
    <link:label id="lab_fgbi_ConsumerAndOtherMember_documentation_en-US" xlink:label="lab_fgbi_ConsumerAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans issued to consumers and other entities not otherwise reported by category.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fgbi_ConsumerAndOtherMember" xlink:href="fgbi-20251231.xsd#fgbi_ConsumerAndOtherMember"/>
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    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract_019bdcae-e261-77dc-8600-cf945d0c94f5_terseLabel_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities:</link:label>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfHeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfHeldToMaturitySecurities"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_019bdcae-e2e9-78ec-886c-3ec749c59023_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Held to maturity, at cost and net of allowance for credit losses of $150 (estimated fair value of $268,094 and $251,458, respectively)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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    <link:label id="lab_us-gaap_CorporateDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Debt Securities [Member]</link:label>
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