You cannot get a more Parisian park than the Luxembourg Gardens. It is situated in the heart of the beautiful sixth arrondissement around St. Germain, making it hugely accessible for everyone. The park surrounds the imposing Luxembourg Palace which is now the seat of the French Senate.
It is so much fun, even as an adult, to rent one of the little sailboats in the main fountain of the garden and push it around with a stick. Most of the time the boats capsize or collide with other boats, but that is part of the fun! (You can rent the sailboats on Wednesdays and on weekends.) There are also pony rides (Wednesdays and weekends) and swings. The ubiquitous Manege (merry-go-round) is a beautiful older-style wooden affair, run by a lovely lady who does not mind kids taking their time to decide on which wooden animal to ride. If you have time, it is lovely to sit at the outdoor café, have a coffee or apple juice and watch the world go by.
I reckon the Luxembourg Gardens playground is the best in Paris because it remains relatively empty as it is the only playground I know of in the centre of the city that charges an entrance fee. The gated playground is large and caters to children of all ages.
Last but not least, and though I hate being so practical, the Luxembourg Gardens is one of the only places in Paris I have found in which the toilets have a changing table and cute, clean, kid-sized toilets with little hand-washing basins.
Emilie writes for Babyccino from Paris.