Fontainebleau to Mont Saint Michel

You probably only have time for one stop.
Chartres would be my pick. It has a beautiful cathedral and town center, has easy motorway access, and lends itself very well to a ~3 hour visit and walk, but it is perhaps a bit too close to Fontainebleau.
Further along you have Le Mans: amazing medieval city with another great cathedral, but it is a bit larger (you'll want to stay half a day) and further from the motorway exit.
Then, the best route to Mont Saint Michel goes north from Laval towards Fougères, and Fougères has a lovely medieval castle, one of the largest and best-preserved in the country. The visit takes about 1.5 hours.

what sort of must-sees do you like?

Will you go up to and along the Normandy coast or travel in a relatively straight line, like via Le Mans or the southerly route via say Orleans and/or Tours?

Will you do this in one day or do you have more time for the journey?

It will be one day, and then we will have a few days in Normandy. So we will take a fairly direct route. Mostly. I like to meander. Our favorite sites are historic. All those listed above by balso sound wonderful. I'm also travelling with a teen and pre-teen, so any experience that might be appealing to them would also be good. So I'm open to many possibilities because you never know what will strike them just so.

It adds a lot of driving time, but I'd consider Fontevraud Abbey, which is certainly historic. It's also about half-way. Vitre is close to your destination, but a good stop that's quicker than a city center like Chartres. Have you already been to a few Chateaux in the Loire?

Not on previous trips. This trip won't be for a couple months yet.

Teen and pre-teen? They'll probably like the castle in Fougères, or the one in Vitré (a great suggestion, but Vitré is a slightly longer detour than Fougères). Conversely, I don't think the city of Le Mans will appeal (but, edited: the 24 Hours museum might!).
I see suggestions like Fontevraud abbey or Loire chateaux: all great but it would take you too far south in my opinion, adding 1-2 hours of driving time...

if you're going in a couple of months - around Christmas?

The days will be really short by then so I guess you'll want to be direct (as you said) and get the driving done during the day, probably by 3.

You may just want to plan a lunch stop and get on with it.

I'd have thought that with the kiddoes a good stop along the way would be Orleans with its associations with Joan of Arc and then a chateau or two, but you won't have time for that. And then you'll be in Normandy so no need to go up that way.

So it looks like its via Le Mans with a lunch stop somewhere.... non-stop it will take you 4 to 5 hours so really not a lot of time to look around...

The winter rain and wind can really rip around Brittany and Normandy. Be sure to take suitable clothing.

With bad weather you can look for something indoors like the Museum of the 24 Hours of Le Mans if of interest ofcourse.