My favorite is the Jardin du Luxembourg, where we were met by a very quick downpour which actually added more to our fun (we were running for shade with our 3-year old twins and fumbling with our umbrellas!) --- but during the summertime, this place is busy with people on the fountain sometimes with toy boats. The parks in Paris also have puppet shows for the kids - I think almost all of the major parks do.
Outside the Louvre, walk onto the Jardin des Tuileries and when I was walking there, I saw a group of school kids having fun in the gardens. It's just nice to breathe in the nice air, thanks to the plants.
There is a nice maze for kids at the Jardin des Enfants aux Halles, 105 rue Rambuteau. And a must for young children is the Jardin de'l Acclimatation Bois de Boulogne (Metro Line 1 to Les Sablons, exit at rue d'Orleans) which has an "enchanted river" with a nice blue Asian pavilion and ice cream stands. The place has pony rides, paddle boats and of course, the quintessential merry-go-round.
These are just some of the green places and just look at the map and you'll see all those other very nice green spots! Enjoy Paris!

