It isn't always clear how reimbursement works in France. For Psychologists, only the "mutuelle" potentially reimburses part of the consultation. In practice can give you an "attestation" to send them, and they will partially cover the costs.

This depends on your insurance provider and you should check with them directly.  

The only psychologists who are fully reimbursed are the ones working in the public sector, in hospitals or structures attached to hospitals (CMP : centre medico-psychologique for example). Psychiatrists can also be reimbursed as they are doctors first and foremost, unlike psychologists who aren't medical doctors.