She is apparently not from the country the games are set in, and often peppers her speech with phrases of French*.
*She speaks French in the English version of the anime, and English in the Japanese and French versions of the anime.
So no, she's not technically French. If you want, you could say that she's French in the English anime, and English in the French/ Japanese anime. She's just not from the country the games/ anime are set it in.