You can take a dunk in one of Paris' public pools. But NOT in the Jardins du Luxembourg Fontaine Médicis. That's an artwork.
You don't have to be a citizen or resident to use the pools. Just pay the fee (tarif - 2,60 euros).Or buy a carnet of 10 entrées just like on the Metro and pay even less.
You say you'd love to go swimming but you left your cap, your goggles, your bathing suit at home. Not to worry.
Weekends are open all day to everyone. The schedule can change too, holidays etc. But there's a printed leaflet explaining all. The pools have private changing cabines. You turn in your clothing and valuables to the clothes check and receive a red rubber bracelet in exchange. Showers are unisex. No big deal. The St.- Germain pool is huge, very clean and refreshing.
My only gripe is the French don't swim in an orderly fashion. They haven't heard of circular swimming. Nor waiting to take your turn in a lane. It's a free-for-all. I do water exercises rather than laps.
You can still get some crème glacée after your swim. Hey you've earned it and already worked off the calories. Well sort of...BTW www.France2.fr is a terrific site to sharpen your Fr. speaking skills and comprehension. At this link click on the Vidéo to see the latest glace fashions in French restaurants.