Birth Certificate issued by Indian Consulate Rejected

Hi. I am an Indian currently doing a masters in France. I am more than 40 years of age and I didn't have a birth certificate till date. So when ameli rejected my marriage certificate, I submitted a birth certificate issued by Indian consulate in Paris, which was in French. However even the certificate issued by consulate is also rejected saying it is "Non standard Certificate" I don't have any other proof of date of birth and parents name other than my passport. As of now I have only my temporary french certificate of insurance.

1. Can you please advise me how I can get my permanent SSN with the documents (Passport & Certificate issued by consulate) I have submitted?
2. Can I continue with my studies& internship without a permanent SSN?

Thank you, Deepak