GOODWILL AND OTHER INTANGIBLE ASSETS, NET - Expected Future Amortization (Details) - USD ($) $ in Millions	Jun. 29, 2025	Dec. 29, 2024
Goodwill and Intangible Assets Disclosure [Abstract]
Remainder of 2025	$ 7.8
2026	15.6
2027	15.6
2028	15.9
2029	15.0
Thereafter	64.3
Net Carrying Amount	$ 134.2	$ 142.0

Finite-Lived Intangible Asset, Expected Amortization, After Year Four

No definition available.

Name:	fat_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour
Namespace Prefix:	fat_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Name Accounting Standards Codification
-Section 55
-Paragraph 40
-SubTopic 30
-Topic 350
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482640/350-30-55-40

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 985
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481283/985-20-50-2

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 985
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481283/985-20-50-2

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 350
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482665/350-30-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 926
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483154/926-20-50-5

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration