A residence permit from another European Union  country allows you to circulate between that EU country and France, but not necessarily to stay in France to study.

We recommend that you double-check  :

 - First, contact the authorities of that EU country where you are currently living and explain that you will come to France to study temporarily, and then come back to finish your studies.

 - Secondly, visit the nearest French consulate in your country of current residence with your residence permit and explain again your situation. 

Please note that even if you get solid confirmation that your permit will allow you to study in France, you may not be eligible for French housing subsidy from the French government.