The only place in France I have seen this happen was Paris and public toilets are free there. I haven't seen paid toilets at all in France for a long time, actually. Maybe in train stations though.
I went to Paris a month ago and saw paid public toilets. Those enclosed things on the sidewalk.
Yes; the inverse is not true; making it free won't ensure that it won't happen.
I've seen paid toilets in train stations (last month in le Mans, a few years ago in a corner of Montparnasse station, though that was before the last round of renovation) and in a mall (CNIT in la Defense). Some RATP train stations have public toilets that you can access with your train ticket, so it's not quite free.