My favorite is probably crepe, which Americans pronounce like an almost diphthong-y craype (or crape like grape I guess) when crep (like step) would do just fine and be closer to the original.
But as a native French and basically-native American speaker, I also couldn't really care less about it, or about things like Americans pronouncing the t in croissant, or French people being unable to say the.
I say it the American way when I speak English anyway because that's just how it is. :)
See also: Cairo, IL or Versailles, KY...
Fontainebleau State Park -> Fountain Blue State Park
These were two off the ones that really stood out from my travels.