Opinions on my proposed itinerary?

Look into bus and train options for Pisa and La Spezia to Volterra. That is the one place where I would want a car, and there should be no problem getting an automatic in La Spezia or Pisa. Milan to CT is fairly straightforward.
Many say Vernazza is not their preferred base in CT--that is gets crowded perhaps more than the other villages and does not have the best restaurants. All of the villages are minutes apart by train, so you may want to look at other bases. You can probably top over in Lucca on your travel day and keep the car in the countryside on your exploring day.

Monterosso is larger so has more hotel and dining choices than Vernazza. If it were my trip I would add more time to Lake Como, then go to le Cinque Terre, stay in Monterosso. I would delete Volterra and the far western Lucca and use those days to go farther east into Tuscany such as Siena.

You are wise to look at transportation before settling on your plan!

It is a very long day to go from Bayeux to Gimmelwald. It is 9-10 hours by train to Interlaken (several changes) and then you have an hour or so to get to Gimmelwald via gondola and train. Flying is no better to get to this mountain destination. Flying is only for a small part of the journey then you have trains for a total of over 9 hours plus time to get to the airport and wait for security, etc.

So a couple of thoughts on that portion:

• Are you really wedded to the idea of one day in Bayeux? Could you stay in Paris and take an escorted daytrip to see the WWII sites, if that is your mission? That alone cuts 3 hours off the train trip to Interlaken. And an extra night or two in Paris is not all bad. Or add a night to Varenna since getting there is also arduous. (See below.)
• Gimmelwald is VERY small with few dining options (maybe one or two?) for dinners. Sure you can go to Muerren for dining, but just saying, it is VERY tiny and 4 nights there seems like a long stay to me. Muerren would provide better options for both lodging and dining. Or stay in Lauterbrunnen and cut some travel time off many of your daily jaunts as well as arrival and departure.

Also, Gimmelwald to Varenna-Esino is another challenging day: 7 to 8 hours in at least half-a-dozen transport methods.

Driving is not really an option in any scenario between two countries unless you fancy huge drop off fees.

A good place to check overall train options is at https://www.bahn.com/en. You cannot necessarily book everything on Bahn, but it is great for researching possibilities.

Vernazza was my least favorite of the Cinque Terre villages. Granted it has fewer restaurant options, but we loved staying in Manarola. We stayed at Aria Di Mare with AMAZING views of the village and ocean. Very good value. Billy's is a fabulous restaurant just down the street from Aria Di Mare. We wished we would have eaten there 2 nights.

We liked Varenna. I would try to add a day there especially since your travel time from Gimmelwald will be quite long.

Logistics wise this itinerary is not easy. Be kind to yourself and remove a country. Getting from one place to another is not going to be fun and no matter how light you pack you can never pack light enough. Expect to be climbing up and down stairs hauling luggage on transport days and you have a lot of them.
If you stick with this itinerary, go to Bayeux on arrival day. I suggest taking a taxi from the airport to the Paris St Lazare station then a direct train to Bayeux (2h 30m). However, you need a car to visit Normandy unless you take a tour and I don’t know if you can rent a car in Bayeux.

There are quite a few car rental places in Bayeux. If you need a car for Normandy (you could do a tour and avoid car rental), I think picking it up in Bayeux is a good plan. As long as you understand that some of the train rides will be long, I think this is a reasonable itinerary.
We took a train from Varenna to CT. I believe it was about 4 hours, we went thru Milan. It was fairly straight forward.

I do like the itinerary, but there are those two incredibly long travel days... I have no brilliant suggestion for you. I'd either develop a burning desire to spend a couple of nights somewhere along the way, or I'd think about substituting the Dolomites for the Bernese Oberland. I think that would cut the travel time, but I confess that I haven't verified that.

I would not treat the D-Day sites as a day trip from Paris. That's too much travel time and not enough time at the sites themselves--unless you're willing to get up really early and take Overlord's Tour #2FS, which is designed for folks sleeping in Paris. You'd buy tickets on the first train from Paris and be picked up by the tour van right at the Bayeux train station. The tour returns you to the train station at the end of the day so you can head back to Paris. (You'd be responsible for buying that ticket, too.) This approach gets you essentially a full-day tour, but it makes for a long day, and I wouldn't want to do it the day before an incredibly long slog to the Bernese Oberland. Taking that tour while based in Paris also doesn't get you any time to enjoy historic Bayeux, see the good local invasion museum, see the Bayeux tapestry or check out the cathedral.

I think for folks truly interested in the invasion who are not experts on the topic, a full-day tour is essential. I'd prefer to do that via at least two nights in Bayeux as you have tentatively planned.

If you have only one day and perhaps a few odd hours on the day you travel up from Paris, there's no need for a rental car, but in case you decide to spend some additional time in Normandy: It's my understanding there is only one car-rental agency in Bayeux, inconveniently located. [<< That is apparently wrong; see subsequent post by jules m.] There are multiple agencies in Caen right near the train station. You pass through Caen when you take a train to Bayeux, so Caen's a good place to get a car. Note, however, that many French rental agencies close for lunch and aren't open at all on Sunday. I have my doubts about the availability of pick-ups on Saturday afternoon, too.

Google maps does show 5-6 rental car places in Bayeux. However, Google maps is not the be all end all, and I believe I only saw one that wasn't on the outskirts. I didn't stay in Bayeux, I stayed in Arromanches so I am not a Bayeux expert.. We enjoyed Arromanches very much, but I wish we'd had another day so we could have seen Bayeux. Caen has a huge museum (too much for me), but the city wasn't that interesting in terms of a place to overnight.

Given your desire to do this trip car free, I've heard the Overload tours are excellent, and I would just do one of those. Likely, you will see more and learn more. I think a full day tour on a day trip from Paris would be A LOT. I think you are better off staying a couple nights in Bayeux.

A couple of your train routes are long, but sometimes after a longer stretch of sightseeing and being on the "go" a long train ride is welcome. We like to bring a little picnic. And the train rides thru Switzerland are stunning. There is a high speed train from Paris to Geneva, and from there its a pretty train ride to BO.

I don't see how Google could be so wrong as to show a bunch of car-rental agencies when there's only one, so I must have misunderstood something posted earlier. I have no personal knowledge of the car-rental situation in Bayeux.

Re. car rental in Bayeux. If you search on Autoeurope, no car rentals come up. However, if you search on google maps, a handful, mostly local independent car rentals and Hertz show up. I don't think any of them are very convenient. Picking up a car in Caen and proceeding to Bayeux is likely the way to go given the convenient car rental offices.

And Acraven is absolutely right on car rentals being closed mid day and Sunday. Often on Saturday, they are closed or open only a half day. We've run into this on several trips. Another issue with a rental car is that you have a car that needs to be parked at night. I love being near the old towns of historic towns so there is a trade off.

When we went to Normandy, it was a part of a much longer trip. We picked up the car in Chartres and returned in Vernon. We had three full days in Normandy and it was fun to explore. We did get lost a few times and underestimated distances. I think with just 1 or 1.5 days, the OP would be better off with a tour. A tour would be more efficient.

Others have already warned you about the travel time that you need to consider.

Bayeux --The amazing Bayeux Tapestry is in the city. It is 900 years old made just after the Norman Conquest of England in 1066. It looks like it was just made. Don't miss it.
Also, you need some time to see the D-day beaches and American cemetery among other things in Normandy. There is a lot to see if you are into military history.

Switzerland is great and very scenic, but one of the most expensive places in Europe.

I can't see spending three nights to see Cinque Terre, it is good, but a bit overrated. You aren't going to Venice or Rome, have you been to Italy before? Those cities are very special.

@jules m-we rented a car through Autoeurope in Bayeux for this fall. I believe Hertz is the only one they support there. Could be wrong on that, but I just checked our reservation and it’s confirmed and viable.

OP-might want to check anyway. When I did the rental, the cars available in Bayeux were more to our liking than Caen.

EDIT: I think there are no cars available to rent! I plugged in two different date ranges and yes, message came back that no cars were available. So maybe Caen is the better choice at this time.
2nd EDIT: I got nervous that maybe they closed so used dates for June2024 and they have cars available in Bayeux. Whew!

Thank you all for your comments! I'm working on how to make it slightly less ambitious, although it’s our first trip to Europe and we are both excited. The part to cut out would be Paris, but geez that's so high on daughter's list. We will consider flying to into Paris and just heading to Bayeux and do Paris after Bayeux to lessen the eventual train trip to Switzerland. In Bayeux my thought was to do one of the ebike tours of the DDay beaches and then on foot exploring the town for the remainder. I’d love to see the beaches, I hate to cut out that part in Bayeux but we could. I do think a long train day could be ok from Paris to ultimately Gimmelwald area.

Maybe take train from Paris to Geneva and then get on the Golden Pass train to Interlaken, with perhaps a night in Geneva to break up the trip? And then to get to Lake Como, either the regional train or we could do the Gotthard Panorama express to Lugano – longer but amazing scenery? I know those will be long travel days. But hey we live in Texas driving 10 hours to get to a good destination is not out of the question.

In Italy, we could get a rental in Pisa as valadelphia had suggested and then explore the hill towns based in Volterra and drop it back in Pisa and then train to Florence for the last hurrah.

We will reconsider our Cinque Terre home base. Thank you for the terrific suggestions, I’m sure this won’t be my last post! I find this all so overwhelming, it’s hard to know what to cut out.