Jardin du Luxembourg

http://www.telegraph.co.uk/travel/destination/france/paris/136765/Paris-free-things-to-do.html

Jardin du Luxembourg (11)

The quintessential park in a city where most people don't have gardens is a hive of activity, with its pony rides, swingboats, sandpits and playground, tennis courts, chess players, early-morning joggers, and the round pond where generations of children have rented toy boats. Originally the gardens of the Palais du Luxembourg (built for Marie de Médicis, now the Senate), one side is French style with gravel paths, trimmed avenues, statues and bandstand, the other English style with rolling lawns (no walking on the grass). Best activity of all? People watching from a pale green Luxembourg metal chair.

This is the quintessential park in a city where most people don't have gardens.

Address: Place Edmond Rostand, 75006 Paris
Getting there: RER Luxembourg
Contact: senat.fr/visite/jardin
Open: daily, varying between 8.15am-4.30pm in December to 7.30am-9.30pm in late June

 http://www.davidlebovitz.com/2009/04/ten-great-things-to-do-with-kids/
The southwest corner of this Renaissance garden is devoted to kids, including acres of slides and swings. It costs 1,50 Euro to enter and espresso is another euro; but sitting in the shade of century-old plane trees while the kids run themselves ragged… priceless. There’s even a hundred-year-old puppet theater run by a crotchety old man. And, of course, the famous carousel.

http://www.theguardian.com/travel/2013/may/10/paris-with-kids-family-friendly 
Luxembourg is quintessential Paris with children, a place that makes it easy to idealise life in the French capital. ... Inside are a massive playground, Charles Garnier's carousel, puppet shows, pony rides and sailboats for hire. We usually stop at the unassuming Boulangerie Marc Rollot, 48 rue Madame before heading into the park. It's become our family favourite for pastries – especially the apricot-and-custard oranais and the pain aux raisins.

http://www.nytimes.com/2013/08/04/travel/travel-guide-paris-for-kids.html?pagewanted=2&_r=1 
Your children can mingle with the offspring of the French cognoscenti at the Luxembourg Gardens (Sixth Arrondissement, museeduluxembourg.fr/en/le-musee/jardin), a park that’s appealing to all ages. There’s an excellent enclosed pay-to-play area (with bathrooms), pony rides and toy sailboats in the central basin. The park’s storied puppet theater puts on shows, in French, daily at 4 p.m., and at 11 a.m. and 4 p.m. on weekends.