Opening a Bank account for non-foreigners

Apparently all you need is a photo ID, a document proving your address (utility bill or similar) and a signature.  No mention of having to prove a previous deposit.

Pick your bank and go see them. It will be tough. If you have proof of an account in your old country that will help. If you have been a cash-only person all your life you will need cash and a good story. If you have a resident card and money they really can't say no (I think) since the country gave you your card. It may take going to the next person at the bank. You should not plead. Here you demand in a respectful way. With Documents in hand like you know what are doing. If they say no ask to see their superior. You need a French bank account and IBAN (account number) to get your Carte Vital. Even though my wife has had an account for 60yrs I could not get the Carte Vital until I had my own account which I could not get until I had my Carte Sejour. The day I laid the Carte Sejour on his desk I had an account in 30 mins. Majic.

That is the law but I have never met a Banker that was not afraid of a person with a cash-only life. I would send you down the street to another bank. My boss would kick my ass if I took you in. And his boss would throw a fit. Bankers that take risks, lose their jobs.