<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2026-03-30T17:23:19.7786+00:00 -->
<!-- Copyright (c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
<xsd:schema targetNamespace="http://www.fbin.com/20260330" attributeFormDefault="unqualified" elementFormDefault="qualified" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:ecd-sub="http://xbrl.sec.gov/ecd-sub/2025" xmlns:ecd="http://xbrl.sec.gov/ecd/2025" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:us-gaap="http://fasb.org/us-gaap/2025" xmlns:dei="http://xbrl.sec.gov/dei/2025" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:fbin="http://www.fbin.com/20260330" xmlns:xlink="http://www.w3.org/1999/xlink">
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/linkbase"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd" namespace="http://xbrl.sec.gov/ecd/2025"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd" namespace="http://fasb.org/us-gaap/2025"/>
  <xsd:import schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd" namespace="http://www.xbrl.org/dtr/type/2024-01-31"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-sub-2025.xsd" namespace="http://xbrl.sec.gov/ecd-sub/2025"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd" namespace="http://xbrl.sec.gov/dei/2025"/>
  <xsd:annotation>
    <xsd:appinfo>
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        <link:definition>75000 - Document - Document and Entity Information</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:linkbase id="lnk">
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension" xlink:type="simple"/>
        <link:arcroleRef arcroleURI="http://www.esma.europa.eu/xbrl/esef/arcrole/wider-narrower" xlink:href="http://www.xbrl.org/lrr/arcrole/esma-arcrole-2018-11-21.xsd#wider-narrower" xlink:type="simple"/>
        <link:roleRef roleURI="http://www.fbin.com/20260330/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:href="fbin-20260330.xsd#DocumentDocumentAndEntityInformation" xlink:type="simple"/>
        <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/PvpDisclosure" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#PvpDisclosure" xlink:type="simple"/>
        <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/AwardTimingDisclosure" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#AwardTimingDisclosure" xlink:type="simple"/>
        <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/IndividualsOnly" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#IndividualsOnly" xlink:type="simple"/>
        <link:roleRef roleURI="http://xbrl.sec.gov/ecd/role/PvpAdjustmentsOnly" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#PvpAdjustmentsOnly" xlink:type="simple"/>
        <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:title="labelLink" xlink:type="extended">
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          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_JohnDLeeMember" xlink:label="fbin_JohnDLeeMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems" xlink:label="dei_DocumentInformationLineItems"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_NicholasIFinkMember" xlink:label="fbin_NicholasIFinkMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_ChristopherJKleinMember" xlink:label="fbin_ChristopherJKleinMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_KristinEPapeshMember" xlink:label="fbin_KristinEPapeshMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_HirandaSDonoghueMember" xlink:label="fbin_HirandaSDonoghueMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_DavidVBarryMember" xlink:label="fbin_DavidVBarryMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInformationLineItems" xlink:label="dei_EntityInformationLineItems"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_JonathanBakshtMember" xlink:label="fbin_JonathanBakshtMember"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Changes in Fair Value to Reflect Excess Fair Value Resulting From Modifications to Stock Option and Stock Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Changes in fair value to reflect excess fair value resulting from modifications to stock option and stock awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_JohnDLeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">John D. Lee [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_JohnDLeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">John D. Lee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_NicholasIFinkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nicholas I. Fink [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_NicholasIFinkMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Nicholas I. Fink.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_ChristopherJKleinMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Christopher J. Klein [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_ChristopherJKleinMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Christopher J. Klein.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_KristinEPapeshMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Kristin E. Papesh [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_KristinEPapeshMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Kristin E. Papesh.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_HirandaSDonoghueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hiranda S. Donoghue [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_HirandaSDonoghueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Hiranda S. Donoghue.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_DavidVBarryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">David V. Barry [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_DavidVBarryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">David V. Barry.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_JonathanBakshtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Jonathan Baksht [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_JonathanBakshtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Jonathan Baksht.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="fbin_JonathanBakshtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Jonathan Baksht [Member]</link:label>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember" xlink:to="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_JohnDLeeMember" xlink:to="fbin_JohnDLeeMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProfitLoss" xlink:to="us-gaap_ProfitLoss_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentInformationLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_NicholasIFinkMember" xlink:to="fbin_NicholasIFinkMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_ChristopherJKleinMember" xlink:to="fbin_ChristopherJKleinMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_KristinEPapeshMember" xlink:to="fbin_KristinEPapeshMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CoverAbstract" xlink:to="dei_CoverAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_HirandaSDonoghueMember" xlink:to="fbin_HirandaSDonoghueMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_DavidVBarryMember" xlink:to="fbin_DavidVBarryMember_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityInformationLineItems" xlink:to="dei_EntityInformationLineItems_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="fbin_JonathanBakshtMember" xlink:to="fbin_JonathanBakshtMember_lbl"/>
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        <link:presentationLink xlink:role="http://www.fbin.com/20260330/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems" xlink:label="dei_DocumentInformationLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInformationLineItems" xlink:label="dei_EntityInformationLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
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          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_EntityInformationLineItems" xlink:to="dei_EntityRegistrantName" order="0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_AmendmentFlag" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_EntityInformationLineItems" xlink:to="dei_EntityCentralIndexKey" order="1" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentInformationLineItems" order="49.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityInformationLineItems" order="50.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
        </link:presentationLink>
        <link:presentationLink xlink:role="http://xbrl.sec.gov/ecd/role/PvpDisclosure" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember" xlink:label="ecd_AllIndividualsMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_NicholasIFinkMember" xlink:label="fbin_NicholasIFinkMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_ChristopherJKleinMember" xlink:label="fbin_ChristopherJKleinMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember" xlink:label="ecd_AllAdjToCompMember"/>
          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember" xlink:label="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems" xlink:label="ecd_PayVsPerformanceDisclosureLineItems"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss"/>
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          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ecd_AllAdjToCompMember" xlink:to="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember" order="4.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="ecd_PayVsPerformanceDisclosureLineItems" xlink:to="us-gaap_ProfitLoss" order="32.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/terseLabel"/>
        </link:presentationLink>
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          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_HirandaSDonoghueMember" xlink:label="fbin_HirandaSDonoghueMember"/>
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          <link:loc xlink:type="locator" xlink:href="fbin-20260330.xsd#fbin_DavidVBarryMember" xlink:label="fbin_DavidVBarryMember"/>
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    </xsd:appinfo>
  </xsd:annotation>
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  <xsd:element id="fbin_NicholasIFinkMember" name="NicholasIFinkMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fbin_DavidVBarryMember" name="DavidVBarryMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fbin_KristinEPapeshMember" name="KristinEPapeshMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fbin_ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember" name="ChangesInFairValueToReflectExcessFairValueResultingFromModificationsToStockOptionAndStockAwardsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="fbin_ChristopherJKleinMember" name="ChristopherJKleinMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
