Allowance for Loan Losses - Summary of Changes in Allowance for Loan Losses, by Portfolio Type (Details) - USD ($) $ in Thousands	9 Months Ended
Sep. 30, 2020	Sep. 30, 2019
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	$ 10,929	$ 10,776
Charge-offs	(1,763)	(2,936)
Recoveries	796	242
Provision for loan losses	4,626	4,148
Ending allowance	14,588	12,230
Real Estate
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	7,815	7,622
Charge-offs	(890)	(1,367)
Recoveries	57	40
Provision for loan losses	3,542	1,747
Ending allowance	10,524	8,042
Real Estate \| Construction & land development
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	423	581
Charge-offs	(265)	0
Recoveries	0	0
Provision for loan losses	300	(58)
Ending allowance	458	523
Real Estate \| Farmland
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	50	41
Charge-offs	0	0
Recoveries	0	0
Provision for loan losses	330	5
Ending allowance	380	46
Real Estate \| 1- 4 family
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	1,027	911
Charge-offs	(108)	(522)
Recoveries	38	35
Provision for loan losses	291	408
Ending allowance	1,248	832
Real Estate \| Multifamily
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	1,038	1,318
Charge-offs	0	0
Recoveries	0	0
Provision for loan losses	(245)	(323)
Ending allowance	793	995
Real Estate \| Non-farm non-residential
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	5,277	4,771
Charge-offs	(517)	(845)
Recoveries	19	5
Provision for loan losses	2,866	1,715
Ending allowance	7,645	5,646
Non-Real Estate
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	3,114	3,154
Charge-offs	(873)	(1,569)
Recoveries	739	202
Provision for loan losses	1,084	2,401
Ending allowance	4,064	4,188
Non-Real Estate \| Agricultural
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	95	339
Charge-offs	(60)	(40)
Recoveries	25	0
Provision for loan losses	97	(177)
Ending allowance	157	122
Non-Real Estate \| Commercial and industrial
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	1,909	1,909
Charge-offs	(240)	(598)
Recoveries	66	21
Provision for loan losses	1,219	671
Ending allowance	2,954	2,003
Non-Real Estate \| Consumer and other
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	1,110	891
Charge-offs	(573)	(931)
Recoveries	648	181
Provision for loan losses	(290)	1,922
Ending allowance	895	2,063
Non-Real Estate \| Unallocated
Allowance for Loan and Lease Losses [Roll Forward]
Beginning allowance	0	15
Charge-offs	0	0
Recoveries	0	0
Provision for loan losses	58	(15)
Ending allowance	$ 58	$ 0

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

No definition available.

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

- Definition

Amount of allowance for credit loss on financing receivable. Excludes allowance for financing receivable covered under loss sharing agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953423-111524

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(7)(2))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=121599878&loc=SL82895884-210446

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121599337&loc=SL82919249-210447

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=121599337&loc=SL82919249-210447

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLosses
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of increase in allowance for credit loss on financing receivable from recovery.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 55
-Paragraph 79
-URI http://asc.fasb.org/extlink&oid=121647567&loc=SL82922352-210448

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=121599337&loc=SL82919249-210447

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(4)
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953423-111524

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of writeoff of financing receivable, charged against allowance for credit loss.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (d)
-URI http://asc.fasb.org/extlink&oid=121599337&loc=SL82919249-210447

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(3)
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953423-111524

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 55
-Paragraph 79
-URI http://asc.fasb.org/extlink&oid=121647567&loc=SL82922352-210448

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of credit loss expense (reversal of expense) for financing receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121599337&loc=SL82919249-210447

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(11))
-URI http://asc.fasb.org/extlink&oid=120399700&loc=SL114874048-224260

+ Details

Name:	us-gaap_ProvisionForLoanLossesExpensed
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=us-gaap_CommercialRealEstatePortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_ConstructionAndLandDevelopmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_FarmlandMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_OneToFourFamilyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_Multi-FamilyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_NonFarmNonResidentialMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivablePortfolioSegmentAxis=fgbi_NonRealEstatePortfolioSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_AgriculturalMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_CommercialAndIndustrialMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=fgbi_ConsumerAndOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_UnallocatedFinancingReceivablesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: