France isn't quite as strict as to make it an instant criminal offence to go overdrawn ( If it were, I'd be in jail, for one!) What used to happen was that the bank wrote a stern letter the first time you went over, warning you of the consequences. The next time you not only lost your bank account but couldn't open another one, anywhere in France. There was a central banking authority, to which the bank reported. Currently they seem to be a little more flexible. I've been over at least twice in recent years and had a fairly polite letter. On the other hand, I've had funds transferred instantly, lest the bank resumes past practice ! They take a sensible view, having regard to the size of the account, the amounts involved, its activity and the fact that a foreigner's account is less likely to be monitored daily by the customer than a local's is.
It is, of course, a criminal offence to issue a cheque (almost non-existent in France) in the knowledge that you have not the funds to meet it.
However, we could have done with French practice on mortgages.Every step is monitored. The applicant has to produce a lot of paper to prove income and outgoings, right down to normal household and family expenses. The lender won't lend any more than a small multiplier of the net income result, and isn't allowed to.It seems that, if they do lend more and the borrower defaults because of that, the loss is on the lender, not the borrower, for breaking the rules.A result is that France has a lot less trouble over mortgages than we, or the US, have had.