To open a bank account, you will
need to show the three following documents:
1- valid passport
2- carte de séjour
3- proof of address: telephone or electricity bill, rent receipt,
certificat d'hébergement (official document stating that you are
staying with a private resident, obtained by your French host
from the local mairie), etc.
Approximately
10 days after opening the account, you will receive a
chequebook and/or a credit card.
Police
spot identity checks 
In France, the police are authorized to carry out spot identity
checks (contrôles d'identité). This means that police officers
can ask to see the identity papers of any person in any public
place (government administrations, the street, railway stations,
metro stations, etc.) to verify their legal status in France.
It is therefore essential to carry documents proving your identity
and right to be in France: passport, visa or carte de séjour and
student card if applicable.
If you fail to produce valid identity papers during a spot check,
you may be taken to a police station for an identity check (vérification
d'identité).
This check must be performed by a police officer from the criminal
investigation department (police judiciaire), who will check with
the police
station (commissariat) nearest to your stated place of residence
to make sure you live at the address you have stated.