That is a very good introduction overall! The only major mistake is in 배우싶으면, which should be 배우고 싶으면. If you want to improve it even further, you may consider a couple points too. "사람이예요" -> 사람이에요("에" not "예" is the correct spelling). This is a minor spelling thing that even native speaker often get wrong. "프랑스어 가르칠 수 있어서" -> 프랑스어 가르칠 수 있으니까. Your original is fine too, but in this context, I think 있으니까 sounds more natural. ~어서 is more appropriate as a direct reason or cause for something, while ~(으)니까 is for background or loose reason. And some sentences are missing the period at the end.

Yes i'm totally serious about this. 같이 연습해요. 열심히 공부할께요 :) 영어-한국어 or 프랑스어-한국어?

Hey if you're serious about language exchange, I would like to be your partner.

I guess that's a good start. 감사합니다 :)

Excellent! Your Korean is very good, even my Korean friend xD