I am french and want to apply for a tourist visa from kolkata. Is it possible?

I think you should contact the CVASC branch in Kolkata to confirm it. As I know, the applicants who apply in the third country or region must provide legal status proof such as resident permit for working or studying.

Contact info:
Contact information
TEL: +91-033-40010210
FAX: +91-033-40010207
E-mail: kolkatacentrevisaforchina.org