For the best colleges in France, an overall IELTS score of 7+ would be preferred although 6.5+ is also accepted by many of the top colleges in France.

So, you are eligible for admission, but for the best colleges and universities such as University of Paris or HEC Paris, you'll need to have a much stronger application in order to compensate for the slightly varying IELTS score.

Additionally, if you are applying for an MBA then you will also need to submit GMAT scores. For most other graduate programs, GRE scores are required although that depends on the course of study (STEM courses always require GRE/GMAT scores). 

In order to make your application even stronger, you could look into certification courses in French or give the French language proficiency exam DELF. Any language proficiency will further make your application more attractive in the eyes of the admissions committee and increase your chances for admission.

Hi. Yes, you are eligible to study in France. Apart from IELTS, you need to qualify in GMAT/GRE and French language test as well. If you meet all the eligibility criteria, then you will be eligibile for the studies.

Thank You!