Although we often capitalize a country or city name when it’s part of a food name, that’s not always the case, and it’s typically not the case with french fries. Most sources say to keep it lowercase.
The reasoning given by the AP Stylebook writers is that french describes the style of cut and doesn’t refer directly to the country. The Chicago Manual of Style also recommends keeping french lowercase because french isn’t being used to literally refer to the country. They give swiss cheese as another example—it’s lowercase because it’s not made in Switzerland. It’s named after a cheese called Emmental, which it resembles and which is made in Switzerland. It is capitalized because the name does relate directly to the Emmental region where the cheese originated.
On the other hand, four out of five examples of the phrase french fries in the Oxford English Dictionary have the word french capitalized, and the entry in the Merriam-Webster online dictionary has french fry lowercase, but notes that french is often capitalized.
Ultimately, it’s a style choice, but I recommend keeping the french lowercase in french fry.
Sources
"french fries." AP Stylebook, online edition. Click this (subscription required, accessed July 29, 2014).
"When not to capitalize." Chicago Manual of Style, 16th edition, online, section 8.60. Click this (subscription required, accessed July 29, 2014).
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