I will study... I have finished...
I will study French while I have finished my IELTS exam.

Is it correct ?

Question

I will study... I have finished...
I will study French while I have finished my IELTS exam.

Is it correct ?

Answer

Incorrect. 
You can say: I will study French WHEN I have finished my IELTS exam 
                                     or
                        I will study French when I finish my IELTS exam.

Cheers!