I'm not sure I'd do Versailles in June with littles. They will be mauled in the lines of the Chateau and there are plenty of nice parks in Paris as nice as Versailles. Take them to the Tuilleries and/or Luxembourg Gardens and rent them model boats to sail on the fountain pool. There are often amusement rides set up in the Tuilleries, perhaps not that early. Both parks have lots of playground for kids and in fact nice playgrounds are the norm at large Paris parks.
Jardin Acclimatation is perfection for this age groups (take your own picnic or eat outside first -- worst food we ever had short of the Airport Hilton was this place). The Fondation Louis Vuitton museum is on the edge of this park. If you visit the museum (and every exhibit we have seen there has been wonderful) you can go into the park for free. Once in the Jardin Acclimatation you can use the playgrounds, view the caged birds and animals and such and there are machines to purchase tickets for the rides. Note particularly what I call the 'deconstructed merry go round' -- Instead of going in circles these horses gallop (on track) through the field. It is really fun.
When in Paris with kids we make a ritual of letting them choose a pastry from a nearby bakery to take into a park for an afternoon snack -- or in an apartment, to take home for dinner. Kids are pretty thrilled with this. An apartment is really great with kids and they can go with you on the morning break run and choose breakfast goodies and also the pastry for dessert. (we usually split them)
The kids might enjoy the Montmartre Mini train and you get to see the place while sitting down.
there are carrousels everywhere. big parks, near the Eiffel Tower, on traffic islands. My favorite is the antique Carrousel at square Batignolles -- your kids are about as old as appropriate for that one, but it is charming.
Walking along the Seine is a real pleasure. in some of the central stretches on the right bank there are climbing devices on the walls that kids love to balance and climb along on.
