Be very, very careful with floating checks in France. Overdrafting is a felony (though usually the real crime is the charge the bank hits you with!) and if you overdraft I think it's 3 times, the bank can simply throw you out as a customer.

The other trick is that many banks (check with yours for details) accept a check on the day it's presented and then process it with a transaction date the day before - so if the check is presented for payment at the bank on the 15th of the month, the funds are withdrawn from your account as of the 14th.

Then, for deposits, the opposite is true. Bank records your deposit as arriving on the 15th, and credits your account as of the 16th. So you're two days overdrawn if you like to cut things close.

The date on the check actually counts for nothing - unless it's old enough that the bank can simply refuse to accept the check.
Cheers,
Bev