Spend half a day (at least!) in Jardin d’Acclimation //www.jardindacclimatation.fr/en It has pony rides, puppet shows, an enchanted river ride, a petting farm etc. There’s a miniature train that runs from Porte Maillot through the Bois de Boulogne to the park entrance.
The Tuileries Garden right next to the Louvre has a decent playground, a carousel (north of the garden, near the Castiglione entrance) and trampolines (not sure if they’re there all year round though).
Jardin de Luxembourg has another stand-out playground with plenty of things to climb and jump on, including metal swingboats and pedal karts, though there is a small cost to enter. There's also a traditional carousel.
The Cité des Sciences is a little out of the way but it’s got to be one of the best museums for kids in Paris. Inside, there’s the Cite Des Enfants where you can book a 90 minute session. There are two options for the Cité des Entrants – one for kids aged 2-7 and on for kids aged 5-12. You should probably buy your tickets online first.
Good restaurants: Pizza Popolare, La Felicita, Rooftop du Mama Shelter and Il Grano