Having returned my cards and cheque book with a letter asking to close my bank account one week later it is still open. How long should it take to close?
Did you send the letter by LRAR using a standard form of words like this?
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In person at a branch? Or mailed? I’d think both of those would take a week at least or longer in France
All I did, some years ago in changing from CA to La Poste was leave it to the new bank. They did everything for me, a completely painless divorce. 
If you have done as @JaneJones said Tony, you have done all that is required. I’d just keep my proof of postage and forget it.