You can take a dunk in one of Paris' public pools. But NOT in the Jardins du Luxembourg Fontaine Médicis.
AND you don't have to be a citizen or resident to use the pools. Just pay the fee (tarif - 2,60 euros).You can 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.
You can still get some crème glacée after your swim. Hey you've earned it and even worked off the calories in advance. 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.