Paris/Giverny/Normandy

This is not a lot of time to see everything you want to see, and I think you will need a car to squeeze it all in, particularly since the beaches and Mt St Michel are not on a rail line.

Sticking within your parameters, my preliminary attempt to hit every sight you've mentioned while minimizing the driving looks something like this:

1. Arrive and overnight in Paris
2. Head to Giverny (1h15), Giverny, drive to Rouen (1h); overnight in Rouen
3. Rouen, drive to Bayeux (2h), visit Bayeux tapestry; overnight in Bayeux
4. 1/2 day morning tour at the D-day beaches; drive to Mt-St-Michel (1h45); overnight in MSM
5. Morning in MSM, drive to St-Malo (1h); overnight in St-Malo
6. Drive back to Paris (or return car in St-Malo and then train back to Paris); overnight in Paris
7. Depart Paris

You can see there's driving every day, there's not really more than a half-day if that for exploring any given location, and you're moving hotels every day. Others will probably have a better idea for how to avoid moving hotels so often (probably the easiest thing would be to stay 2 nights in St-Malo, since MSM is not too far) but keep in mind that minimizing hotels will only add to the driving because you'll be doing more driving back-and-forth.

If this were me, I would cut something out (probably Rouen and Giverny, because they're the closest to Paris and thus the easiest to fit in on future visits).

Another possibility is that we rent a car at CDG when we fly in that first morning and given that we will be tired and jet-lagged, drive the shorter hop to Giverny, see the gardens in the afternoon, eat, rest, stay one night (see the gardens briefly again in the morning light before the tourist buses arrive) and then drive to wherever our base of operations in Normandy will be, stay 3 nights, and go back to Paris for 2 nights before flying out, which might also give us a bit more consecutive time in Paris instead of one night on the front end and one night on the back end...

Seasoned France travelers, can't wait to know your thinking here. Much appreciated.

Definitely need a rental car for this. You're wise to overnight in Paris before attempting any distance driving, safety.
Home base in one of towns/cities near D-Day beaches.
Many take train from Paris to city/town in Normandy area and rent car there, renting car in Paris not good.
Suggest you study travel times between all your destinations, esp. the ones you'll drive to/from.

You're really trying to do too much in too little time, but here are my thoughts--with the caveat that I have never driven in Europe, and that is different from depending on trains and buses.

I think a half-day tour of the invasion sites is not a great idea. It is better than just driving yourself around and looking at beaches, but the fact is that Bayeux is a fair distance from the invasion sites, and if your tour is only 1/2 day, a really substantial part of that time will be spent just driving back and forth. A full-day tour gives you a much larger percentage of time actually seeing the invasion sites. If you just cannot afford that much time, I'd suggest going to the WW II museum in Bayeux instead. It's modern, full of English-language explanatory material, and quite good.

You don't really have time to do anything in Paris on this trip, so I think it's a shame to have two one-night stays there. Heading into the city on your arrival day (jetlagged and probably seriously sleep-deprived) doesn't really get you much of anything. I wonder whether there'd be a way to do the trip in reverse of what andrewesque has so carefully laid out. What if, on your arrival day, you took the train to Saint-Malo (or at least as far as Rennes, if car-rental options in St-Malo are not good). That would make some use of time on the arrival day when there's an excellent chance at least one of you will be really struggling to stay awake. That would buy you a few hours, and on a trip as compressed as this one, a few extra hours are worth trying to find.

Edited to add: Go to ViaMichelin.com and check out the driving time it estimates for each of your travel legs. Remember that VM's times are just the beginning. They do not cover stopping, getting lost, looking for parking, walking from the parking place to what you actually want to see. Nor do they account for time spent packing up, checking out and checking into the new hotel. Nor your actual sightseeing time. (Rouen has quite a large historic center; it takes time to see it even if you don't care about any of the local museums.) You'll also need to eat at some point(s). I suspect you'll find there isn't one central place you can use as an efficient base. I hate one-night stops, but I think your best bet here is to plan a sort of loop and keep moving forward. However, I don't have the experience of trying a hub-and-spoke trip by car.

Here's what I'm now thinking, as I dial back a bit on some of these plans.

Day 1: We arrive at CDG at 7:00 a.m. We do the airport routine, go through customs, rent a car, etc. and drive to Giverny. We see the gardens in the afternoon light, rest from jet-lag, eat, and spend the night. [estimated driving time CDG - Giverny: 1 hour 9 minutes]

Day 2: We get up early and maybe see the gardens once more in the morning light, before tourist buses arrive. We then drive to Mont St. Michel with a stop in Rouen for lunch, the Cathedral and a bit of the town. We arrive in MSM by evening. This is kind of an intense day, I know. [Giverny to Rouen 57 minutes; Rouen to Mont St. Michel 3 hours]

Day 3: MSM, resting, enjoying, spending another night here; possible day trip to St. Malo.

Day 4: Leave for Bayeux in the a.m.; see beaches; visit tapestries (open till 6:30 p.m.), spend the night. {MSM to Bayeux 1 hour 40 minutes]

Day 5: Leave for Paris in the a.m., arrive early afternoon. Enjoy Paris. Spend the night. [Bayeux to Paris, 3 hours]

Day 6: Day and night in Paris

Day 7: Fly out for Iceland

Rouen and Giverny are at one end of Normandy (Northwest), and Saint Malo and Mont-Saint-Michel are at the other (Southeast)—with Bayeux roughly in the middle. That being the case, you will minimize some of the driving by putting Bayeux in the middle of your trip rather than one end.

You can see some of the Battle of Normandy sights in a half-day without a tour (not referred to as an “invasion” by the locals, but instead a “liberation”). If you are primarily interested in the American sights, a simple circuit would be to drive out to Longues-sur-mer gun battery high on a bluff overlooking the English Channel which, although taken by the Brits, did a lot of damage to the beaches and the forces at sea. Then drive to Omaha Beach and look back at the bluffs and the four “draws,” or planned exits off of the beach (these were too defended to be taken from the beach as planned, and the assault forces had to go up the steep, mine-strewn bluffs to take the defenses from behind). Drive the length of Omaha Beach and head up the road to the American cemetery on the bluff overlooking the beach. From there, drive to Point du Hoc, which was the gun emplacement the Rangers took by scaling the cliffs. Then back to Bayeux. It is a long half day, but total drive is one hour twenty minutes. To scale it back somewhat, you could regrettably cut out Point du Hoc to make it an hour total driving time. Of course, if you had a whole day, you could include a trip to Utah Beach and the inland areas where the Airborne operation occurred.

A similar half-day to British areas could include Arromanches to see remains of the artificial harbor, Pegasus Bridge where the Brits crash landed gliders to take this bridge in the earliest hours of D-day, and a visit to the Commonwealth Cemetery in Bayeux.

While there are wonderful museums in the area (and some not so wonderful), it seems a shame to spend too much time indoors rather than out where the action occurred. Instead, use the time between now and your trip to learn more so you can see and appreciate more. However, for a good, and convenient overview, you could take in the Bayeux Museum without eating up too much time.

I have never been to Giverny, but reading others’ posts here, it seems like committing your entire first day, plus part of your second day on this one place is giving it too much time given all the other things you want to see.

My too sense…