It might be the best-known park in Paris, but it is one of our favourite places to go. You cannot get a more Parisian park than the Luxembourg Gardens.
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 it capsizes or collides with another boat, but that is part of the fun! (You can rent the sailboats on Wednesdays and on weekends.)
I reckon the playground is the best in Paris and is actually relatively empty as it is the only playground I know of in the centre of the city that charges an entrance fee. There are also pony rides (Wednesdays and on weekends) and swings. The ubiquitous Manege 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.
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.
(Image found here)