You'd be surprised actually. When my wife and I were still dating we decided to do a "slumming it in Paris" vacation. Basically, bedding down on the streets or the parks. It was interesting to say the least. We didn't get much sleep, bedding down late and we hit the streets early each day. We'd keep our stuff in a train station locker and wander around the rest of the time.
To solve the shower problem we'd go to public indoor swimming pools. We'd do a dozen laps in the pool and then use the shower facilities to get a proper wash. I was very surprised to see that the Frenchmen didn't take off their bathing suits while washing. Instead they sort of pulled them out and soaped their privates and rinsed the soap away without ever exposing themselves. They were a little shocked to see me buck naked in the shower getting clean properly. I'm not a very modest person. My wife had a similar experience in the lady's shower.
I don't have any sort of rationale to offer as to why this was. When we lived in the south of France near the Med, it was very common to see women go topless and in some places (one spot near St Tropez in particular) the people ran around naked on the beach. Maybe it's just a Parisien thing? Who knows?