Renewing a different type of passport

Hello,

I am going to Shanghai in April on exchange. My F will be good until end of July. It is my intention to find an internship while I am there for August until December (5 months). I have not yet found the company, but should do surely by June. The guy at the department in Paris (I am French) says an internship visa is not considered an F, but something else.
After this, I will be on exchange again from January until June (so, an F again I would suppose).
Could you let me know what the best way for both renewals is?
Thanks so much