Answer:
Every person is different, and as we do not know this "french person", we cannot tell you for certain. However, some advice I would give:
1) Immerse yourself in french culture so you can have things to discuss.
2) Share with them aspects of American culture that they may be interested in so you can exchange.
3) If they appear cold, continue to be friendly and warm, but if they are uninterested, do not insist.
4) You mentioned you know french. If you speak it fluently, that should facilitate conversation/communication. If you are fluent, read french books, watch french movies/shows, etc. I am french, so if you want I can provide recommendations !
5) If you both participate in an activity together, try to engage and interact with them (but this applies to anyone you want to befriend).
6) Ask them questions to show interest and curiosity.