Hi, one of the best parks for, climbing frames, sand pits etc in the centre is at the opposite end of the Champ de Mars gardens from the Tour Eiffel, there are also a couple of smaller ones in the gardens. Also a small track with with little peddle go karts and push around bikes for the smaller children, and donkey rides (there late on in the afternoon if the weather is good). Nice to go and have a look at the Tower and then a play in the park.
The Tuileries gardens are good for them to run around in (although the play park in there is not that great), and they have trampolines in the park and donkey rides. If you are going in July and August there is a fair in the gardens with some rides suitable for young children. There are also ponds with toy sailing boats you can hire at the end of the park nearest the Louvre.
The Luxembourg gardens have a great park for children - all sorts of slides, climbing frames etc (with a small entrance fee), but you would probably spend at least half the day there which may not be a good use of your time if you are only there a couple of days.
If you are planning on visiting Montmartre the little tourist train that takes you up and down the hill from Place Blanche is good, less tiring for the little legs (and long ones!),www.promotrain.fr/gbaccueil.htm. Also the funicular as Lizcat has said.
Sounds really touristy but a boat trip along the Seine is usually enjoyed by children, and a good way to see a few of the sights without walking too far.
Your 4 year old may like a trip in the hot air balloon (tethered to the ground) in Parc Andre Citroen, but it is a bit out if the way and the balloon only goes up if the weather is good enough. The parc itself is a great, safe place for a run around and a picnic - but as I said maybe a bit out of the way if you are only there a couple of days.
A walk along a section of the river looking at the houseboats and waving at everyone on the tourist boats, nice to picnic on one of the pedestrian bridges or in the Square du vert Galant, the little park on the tip of the Ile de la Cite.
The L'Orangerie with Monet's Water Lilies - even for small children is great to look at the paintings with all the different colours changing as you look around the rooms.
If the queues for the Tour Eiffel are too long to go high up you can go up the Montparnasse Tower. Usually no queue at all and a great view of Paris (with the advantage that you can see the Tour Eiffel as well). It is easy to get to but there is not much else around the area, especially for children.
If the weather is good the self service restaurant on top of Printemps store is reasonably priced, and you can sit outside on the roof and look at the sights whilst eating (or good even for a coffee stop).
Finally the children may like to go around on the open top buses if the weather is nice - not sure about the costs though but a nice way to see some of Paris and usually enjoyed by the kids
Just realised you have been to Paris many times before so apologies if these are things you already know about, but hope some of it is useful