Unfortunately, the Carnavalet is closed for renovations.
For a few museums that may not have occurred to you: Maybe go to the Grande Galerie de l’Évolution in the Jardin des Plantes (don't worry, the Galerie is indoors) and/or the greenhouses at the same Jardin.
The Musée du Quai Branly (non-European civilizations), near the Eiffel Tower, is full of all kinds of interesting and unusual things to look at, but as I recall it can be a bit dark (literally) and atmospheric in places--though I could be misremembering--so I don't know if that might freak out the little one.