You could go with a lycee program.
Not sure how it’s done when you’re not part of an exchange program like nacel or rotary.
You should not enroll in university as you’d lose freshman status and the scholarships that go with it. Only exception is if you enroll in a non credit language program but for a year it may be a bit much. You’re allowed to work 20 hours with your student visa bit work is scarce, so don’t expect to make any money.
I know a program you could enroll in but I need to check how to proceed.
What’s your current level of French - AP, IB SL, IB HL…?