A mistake I always do in English is to say “capacity” rather than skill. It seems like a good and suttle word that your character could say without appearing stupid nor funny.

Not exactly what you had in mind but your question reminds me of sacrebleu that has become a stereotype for French people in the US, since Agatha Christie had Hercule Poirot say that word in her novels, but no French people would ever use that word nowadays (and they didn’t either when Agathie Christie wrote her Hecule Poirot novels).

Maybe in that line you could have your character swear in French, and say something like :

• Merde alors!.
• Putain! (if you have him come from the south of France).
• Zut alors! (which is be milder that the previous two and not rude).

Having understood that “And she flies over the market” (Et elle vole, par dessus le marché”) or “eventually” grossly used for “éventuellement” is not what you want, the best I could advise is to look for Web pages called “faux amis” or the equivalent for English. That’s where you’ll find the most subtle stuff.
Or, if you prefer them obscure, you can invent them yourself, like, keeping in line with the above, in reply to “you’re a twit”, saying “you’re a twat” after the French word “con”.

You could have your character use he or she when referring to some inanimate objects instead of the proper it. Native English speakers would never do that … in fact they tend to be puzzled by the lack of a actual rule when deciding the gender of things.