Though this is not strictly something you can do in Paris with small kids, I do have to sing the praises of something that has very quickly become a Parisian institution: The Velib‘.
You see, all over this wonderful town you can find bicycles belonging to the city council. With a swipe of a card that costs me all of 25 euros a year, I can jump onto an elegant grey bike and cycle (in my case kamikaze style) to my destination. There I find the nearest point and drop off the bike. Nothing could be easier.
The Velib is now as much a mode of transport as the metro and the bus. It is really interesting to see how every Parisian from every walk of life has taken too it.
It is a bit harder, though possible, to rent the bike out as a tourist with a credit card. The instructions are not easy to follow, but if you persist you will get there and it is so much fun exploring Paris via bicycle and not being restricted to the metro.
The problem is that there are no children’s seats on the Velib’. Though I have once or twice seen a kid sitting in the basket mounted at the front of the bike, it is definitely not something I would recommend! Just wait until the kids are a bit older and you can get them a bike of their very own.