Reimbursements

With some limitations, yes. If you are employed, your coverage starts from the first hour of work and you can get reimbursed later. If you are unemployed it's more complicated but you should get coverage from the day you deposit your dossier.

You should make sure to declare your medecin traitant with the appropriate paper form, since it cannot be done electronically.

You cannot get a mutuelle as long as you don't have a Carte Vitale or at least an attestation de droits, so the part not covered by the securité sociale cannot get reimbursed in the end (as citizen, it is common that we pay for the delays of the administration).