Normandy and Mont St Michel

How many days will you be in France, exclusive of travel days to and from?

We will be in France around 9 days.

We did this with our kids a few years back. MSM can be done in one day (though I'd love to spend the night on the island). Normandy can be fit into whatever time you have, but that might mean flying through some sights. I think a minimum of 4 days to get a base understanding of the area.

We stayed in Bayeux ( great little town), We did a full day tour of the Beaches of Normandy - our guide worked for Overlord Tours and he was excellent.
( We went to 3 different beaches and to the American Cemetery)
He was also our guide the second day - we went to Mont St. Michel.
He picked us up each AM at our hotel.
There were 8 of us, but had a whole van and guide to ourselves both days.
(our guide was a young man named Adrian (he went to high school in the US) and spoke English (perfectly - and a charming guide))
I had been to this area before - but having a full day tour at each site really made a wonderful trip for us

Our group just did this during our trip last August.
We did it in 2.5 days with 2 nights in Bayeux. We booked an AirBnB there.
The one thing I would URGE you to do is pay for a Normandy Tour.
I am very frugal, but this was money WELL spent, and your teens will get a Great history lesson. We used Alan Bryson of First Normandy Battlefield Tours. He was fantastic. You'd think he had landed with the troups and knew all of them. (Close, he interviewed many of the survivors.) You can find reviews at Tripadvisor (many of which mention teens) and even my Sept 5 review is still there:
https://www.tripadvisor.com/Attraction_Review-g187181-d2661109-Reviews-First_Normandy_Battlefield_Tours-Bayeux_Calvados_Basse_Normandie_Normandy.html

If you can't get Bryson, Tripadvisor has other reviews of good tours, but I'd say he's perfect for your group.

He will pick you up in his minivan, and it will be roughly 9am to 5pm.
http://www.firstnormandybattlefieldtours.com/
As for your other questions, here's what else we did:

We took the Train to Bayeux around noon (leaves from Gare St. Lazare in Paris)
Early afternoon -- Arrive Bayeux, find lodging, then visit Bayeux Tapestry and WWII museum in town (discount for buying the two tix together).

Next day Normandy Tour with Alan Bryson

Following day-- Mont St. Michel. The Hotel Churchill has a van that goes to MSM for the morning and is not just for Hotel clients. I think it's $65 each. Sign up in advance on Hotel's website. Here are my notes on it:
8:20 -- Shuttle to Mont St. Michel. Meet shuttle at Hotel Churchill, 14 - 16 rue Saint Jean 14400 Bayeux Hotel will store your luggage if you want.
10 AM -- Arrive at Mont St Michel
3 hours browsing Mont St Michel (tickets include tour of the Abbey)
1:30 -- Depart Mont St Michel
3 PM -- Arrival at Bayeux
Evening -- Train back to Paris.

You could rent a car to get to Bayeux and MSM, but even so, take the professional tour instead of driving Normandy on your own. You won't know what you're looking at or what happened there, but Bryson sure does.

MSM is a fabulous place to spend a night. The tides, sunset, sunrise, the mount in the evening when the crowds are gone! You can just walk around, up and down, enjoying the isolation and views!

A stay of 3-4 days in Normandy would be good to discover various aspects in Calvados, around Etretat and in La Manche or Orne (of course if you had a week it would even be better!). Since MSM is on the western side of Normandy, a pleasant extension would be to enter Brittany, at least to see St Malo / Cancale or Fougères, which are not far away from MSM. Renting a car allows you to visit more places and to reach smaller towns. If you take the train, you would have to consider cities/towns like Caen, Bayeux, Granville, Pontorson (to reach MSM), Dol de Bretagne (+ St Malo?), from where you can take a TGV train back to Paris.

I start with what I want to see to decide the number of days. Two sights a day is a good rule of thumb for planning, you can always add lesser sights and evening activities if you have time and energy. I travel light and possibly faster pace than most people would be comfortable with. Since I now travel alone, I only see the sights that I'm interested in.

For me Normandy went like this: Early morning train Paris to Rouen, walk Rouen and lunch, rental car to Etretat, photos of Etretat and Fecamp, night in and Etretat Airbnb. I skipped Honfleur because I had many small port towns planned later in Brittany, otherwise I would have included it as a stop.

Drove from Etretat to Bayeux, early morning, to see the Tapestry. Lunch in Bayeux. I'm not really a fan of more modern history so skipped the D-day tours/sights. Drove to Mt. St. Michel, arrived early afternoon with enought time to climb the ramparts to the Abbey, tour the Abbey, then take my time coming back down through the town. I left late and stayed in nearby Cancale (in Brittany).

I ended up spending much more time in Brittany then biked through Loire and trained back into Paris.

The places I would have added are Caen and Honfleur. Most people have more interest in WWII than I do, so would probably want to add a day or two just for D-day sights.

Thank you everyone for all of the valuable information. We decided to extend our trip a bit. We are taking the train from Paris to St. Pierre des Corps and will rent a car there. We will stay in Amboise for a few nights then move on to MSM for a night so we can really experience the island city. We are staying 3 days in Bayeux. We plan to book a guided tour of DDay monuments etc, as recommended, to maximize our experience. We plan to keep the car until we return to CDG. Does anyone have advice or concerns about renting a car?

If you've never driven in France before I highly recommend listening to this episode of the Join Us in France travel podcast. I learned a lot of things I wish I had known before we went to Normany/Loire last May.
https://joinusinfrance.com/driving-in-france/

Does anyone have advice or concerns about renting a car?

We used AutoEurope a few times and have been happy with them. Most cars are stickshift so if you want an automatic you may have to pick it up in a larger city. We get the 0-deductible coverage for peace of mind. Always carry some euro coins and small bills with you to pay tolls since your US credit card may not work. Strongly recommend bringing a GPS with you so its one you know how to use and that has english directions (be sure to always keep it out of sight when parking your car). We have never had a problem with theft from the car, it is rare, but tourists are a prime target so keep everything in the trunk out of sight and never open the trunk when parking so people can see all your luggage.