Four days outside of Paris

To my opinion day one is busy, but doable. Day two is too much, I would take the time needed to visit the D-day beaches and then heading to MSM. If possible visit in the evening or early next morning before going to Amboise for visiting a few châteaux the time left before going back to Paris. On the spot see how much time left for a bike ride.

Thought about combining Bayeux with the Tapestry?

Most people spend a whole day between DD beaches (several sites) and Bayeux. You can see MSM pretty quickly, but it would better to sleep there than to try and push on. Or, you could cut MSM to focus on the other areas and reduce driving.

I agree with Wil, day one looks possible but rushed, day two is way too much.

I'd suggest sticking to Normandy and MSM, save the Loire for another trip when you can spend more time there chateaux viewing, bike riding, and vineyarding.

The Bayeux Tapestry was a highlight of our last trip, well worth a couple of hours with the exhibits or even a half day. The Normandy invasion in reverse 900 years before.

I don't think it's possible to see DDay Beaches, Mont St Michel, and drive to Amboise all in the same day. Getting to and then seeing either DDay Beaches OR Mont St Michel will basically take a day, and that's not counting a drive onward to Amboise. Unfortunately your Normandy sights are too far from the Loire Valley sites. You need to pick one locale or another with only four days.

Rome2Rio might be a good place to start. You can get some idea of drive times and costs between your locations. Not sure exactly how accurate it is, but it can generate some numbers for you quickly and easily. We're checking it to ballpark train vs car as we plan a two week trip to France for 3. Good luck.

I think it is way too busy. If you do all these things it will simply be a drive by. I think the beaches require plenty of time simply to absorb and think about all that happened there. Also MSM will probably be crowded in the afternoon so if you par, take the shuttle over, return and drive on it will leave little time to even walk around. I would make sure to stay a night on MSM and also a night in Bayeux to see the tapestry and visit the charming town. That is close to the beaches for an easy drive.