Segment Information - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended
Mar. 30, 2025	Mar. 31, 2024
Disaggregation of Revenue [Line Items]
Total revenues	$ 518,309	$ 513,916
Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	173,881	191,251
Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	48,056	47,153
Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	228,941	217,512
Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	23,757	20,935
Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	43,674	37,065
Operating segments
Disaggregation of Revenue [Line Items]
Total revenues	511,093	512,197
Operating segments \| Domestic Company-owned restaurants
Disaggregation of Revenue [Line Items]
Total revenues	170,795	176,224
Operating segments \| Domestic Company-owned restaurants \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	170,795	176,224
Operating segments \| Domestic Company-owned restaurants \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| Domestic Company-owned restaurants \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| Domestic Company-owned restaurants \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| Domestic Company-owned restaurants \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America franchising
Disaggregation of Revenue [Line Items]
Total revenues	36,811	36,746
Operating segments \| North America franchising \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America franchising \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	36,811	36,746
Operating segments \| North America franchising \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America franchising \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America franchising \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America commissaries
Disaggregation of Revenue [Line Items]
Total revenues	264,376	252,554
Operating segments \| North America commissaries \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America commissaries \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America commissaries \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	264,376	252,554
Operating segments \| North America commissaries \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| North America commissaries \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Operating segments \| International
Disaggregation of Revenue [Line Items]
Total revenues	39,111	46,673
Operating segments \| International \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	3,086	15,027
Operating segments \| International \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	12,504	11,456
Operating segments \| International \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	16,022	14,225
Operating segments \| International \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	3,284	3,064
Operating segments \| International \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	4,215	2,901
All Other
Disaggregation of Revenue [Line Items]
Total revenues	74,331	65,207
All Other \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0
All Other \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	0	0
All Other \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	0	0
All Other \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	25,078	21,524
All Other \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	49,253	43,683
Elimination of Intersegment Revenue
Disaggregation of Revenue [Line Items]
Total revenues	(67,115)	(63,488)
Elimination of Intersegment Revenue \| Company-owned restaurant sales
Disaggregation of Revenue [Line Items]
Total revenues	0	0
Elimination of Intersegment Revenue \| Franchise royalties and fees
Disaggregation of Revenue [Line Items]
Total revenues	(1,259)	(1,049)
Elimination of Intersegment Revenue \| Commissary revenues
Disaggregation of Revenue [Line Items]
Total revenues	(51,457)	(49,267)
Elimination of Intersegment Revenue \| Other revenues
Disaggregation of Revenue [Line Items]
Total revenues	(4,605)	(3,653)
Elimination of Intersegment Revenue \| Advertising funds revenue
Disaggregation of Revenue [Line Items]
Total revenues	$ (9,794)	$ (9,519)