If you happen to be in Paris for the month of August (most Parisians have left for the country and the city is spookily quiet) Paris Plage is the place to be. It has something for everyone: bars, a swimming pool and a great play area.
If you go in the mornings the “beach” is relatively quiet, even on the weekends, and it is a perfect place for kids to get rid of some excess energy. This year the place to be for kids is the area around the pont de Sully at the eastern edge of the beach.
The other area of Paris Plage around the basin de la Villette is great too, there is even a sailboat you can rent! I loved the idea of sailing around a canal in the middle of Paris, but so apparently do a lot of people so it is completely overbooked. If you have kids from 6 years upwards, there are some fantastic little pedalos that they can peddle around in, in a supervised area of the canal.
All of this has been sponsored by the Mairie of Paris so almost all the attractions are free!