Generally speaking, the lowercase spelling has the upperhand (ho, ho, ho)
But according to Google books Ngram, the Brits use either indistinctively.
However, Ngram is not really indicative of spelling preferences because many of the results are from book titles, where it is conventional to capitalise nearly every word. e.g More Than Just French Fries, Who Ate My French Fries?, and French Fries: The Ultimate Recipe Guide etc.
So lets take a look at Google Scholar and find out what they have to say
Again, I suspect that many of the uppercase results are tied to titles.
Conclusion? Neither is wrong, go with your personal preference.
More references, and support. Yikes! I am about to cite Grammar Girl (a few venerable members on EL&U consider her “tips” to, erm... lack authority). Miss Mignon Fogarty writes
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.