I read a lot of horror stories about taking kids to the Louvre, but our kids managed it fine and for a few of them it was one of the highlights of the trip.
We didn't try and overwhelm them, so we stuck to a quick pass of the Mona Lisa and then went up to Napoleon's apartments (which isn't as crowded). After that we strolled through a number of the sculpture gardens and then left a little bit after lunch.
The outside of the Louvre is just as grand, so they got a little bit of culture in there as well :)