I would see what is most important to you and your child.. and not on the tour( some people have suggested places you will see on the tour.. so check the daily itinerary so you don't double up) .
I have taken my 11 yr old dd to Paris.. as well as my 13 yr old son( my hubby took our 14 yr old ) We chose to do one on one visits with our kids.. ( smart me got to take the first child,, then hubby took second.. ha ha.. having three kids.. I got the next trip.. so got to take two trips with kids)
I personally think you and your child would love to do a Fat Tire Bike Tour.. the night one INCLUDES a cruise on the Seine.. And , if you really want to see Versailles.. then they do a bike tour there.. its not cheap, but its fun, easy, and you will visit a market , buy picnic goodies and sit at the foot of the canal with an amazing view of the palace and munch away.. before entering the busy palace. The palace will be VERY crowded.. like heaving.. so do consider long and hard if you want to see it ,, or just think you should see it. Remember.. on the BOE tour you will be inside other chateaus.
I agree with poster who suggested Invalids Army Museum.. all my kids loved it.. and I have now been to it four times.. its a lovely museum.. never crowded,, good ac,, and its interesting for kids.. armour, battle axes, swords, etc,, not like a typical art /painting /sculpture museum.. which many kids do not enjoy very much. However.. that said.. my kids also enjoyed Louvre, and Orsay.. ( but we had more time then you and you will see Louvre on tour)
If you elect to do a boat tour on your own its easy.. they leave every hour or so.. you can check out the weather and buy tickets same day or just before boarding.
Mont St Michel( you are correct that it is pronounced "Michelle" but it is spelt "Michel" ) .. unfortunately is out.. while physically possible, its a LONG day.. it should be best done as an overnight.
You are going to have an amazing time on the tour.. really..!!