Paris has many beautiful parks, ranging from huge and grand to tiny pocket parks snuggled in beside churches and apartment buildings. You can stroll or picnic or simply people watch. For little ones, there are plenty of slides and sandboxes (although as I have mentioned before precious few swings) And if you're willing to shell out some dough, there are also merry go rounds, cafés, puppet shows, and pony rides. (Plus cotton candy, ice cream, and balloons.)
In the Luxembourg Gardens, kids can rent a sailboat that they can push with a stick in the large central fountain, and on the Champ de Mars, the preschool set can take 7 turns in a pedal car around a makeshift racing oval for the grand sum of 2 euros.
If you want to be prepared, bring your own paddles and balls for a rousing game of ping pong or a round of foosball.
And if you really can't drag yourself away from the Web, bring your laptop like this fellow. Since 2007, the city of Paris has been offering free WiFi in some 260 places around town. Personally, I'd rather leave the computer at home but hey, to each his own.