Well, looks like this is really happening. Sending the ex-landlord a final request by registered mail for my deposit back, else I'm taking it to court.
Funny how helpful the French government with this: they have an entire page [service-public.fr] detailing what can and can't be done — with a a letter template.
And a bit of googling shows that having to fight to get the deposit back is indeed a frequent problem in France…(what isn't?)