There’s an Android app for that: “Toilets in Paris”. Seriously!
Wish I’d known!
Rule of thumb: use one if you find one... every time. :)
The only “free use” toilets I saw were on Portobello Road in London, on the street fair. One was broken, the other had a line a mile long (frightened me what the insides might be like). So we went into a cafe, got some coffee (the Brits STILL can’t figure out how to make good coffee) and used their nice, clean facilities.