Normandy, France

I would do Giverny as a day trip from Paris separate from Normandy.
Just to give you an idea over a period of 4 days:
I took the train from Paris to Rennes and than a bus to Mont St Michel
I then went from there to Bayeux and toured the American Cemetary and Utah beach.
I actually accomplished this as a solo traveler on a budget by taking the public bus which has limited service.
There is also a public bus that goes to Arromanches from Bayeux.
But you have to do the research.
You may consider trying Bayeux to Rouen on the way back to Paris but this could be too much as I found out.

Once you get off the rail line, getting around is going to be more time consuming/less convenient without a car. I trained to Rouen, looked around, picked up a car and drove to Etretat before heading south to Bayeux and MSM. With a car, it won't be hard to do it all in four days.

I believe Giverny to Rouen will be accessible by train. If you can't do it as a daytrip from Paris, plan it first thing in the morning, then continue to Rouen by train to start your normandy loop. Also consider picking up a car in Giverny. Use viamichelin.com to estimate driving times but figure theirs are minimum times, average driving times are typically a little longer.

Vernon (the stop for Giverny) is on the same rail line that goes to Rouen. Four days will be tight, even with a car; I'd get the car in Rouen.

I rented a car in Rouen and drove to Bayeux, where I spent 2 nights. From there I toured Arromanches Beach and museum, the the Longue-sur-Mer Gun Battery, the American Cemetery and Visitor’s Center at Omaha Beach, and Pointe du Hoc. I also spent time visiting the museums and sights in Bayeux. From there I drove to Mont St Michel and arrived in the afternoon and visited there in the early evening. It’s less crowded, and looks great with the lights at night. I spent the night at a nearby B&B. The next day I drove back to Rouen and took a train back to Paris.

Bayeux is a charming city and convenient to the Normandy beaches. I stayed with a wonderful family in an Airbnb; they clearly enjoyed having guests.

Rouen is a bit tricky driving in due to many one way streets. Others have suggested taking the train to Caen and renting a car from there. You could also rent in Bayeux, but have fewer options.

If you are confident you'll have other visits to Paris, I'd hold Giverny for an easy daytrip from Paris. However, you certainly want to see the gardens in season. Because you have 4 days, you are better off with a car-you can make the best use of your time. Part of the issue is whether you have the budget to pay guides (I mean like those who cater to Americans who think the only point of Normandy is the American invasion .... ) for both transportation and comprehensive tours. Many people have written here about the day-tour to MSM from Bayeux run by the Churchill hotel. We didn't use it, but because I don't believe it's necessary to spend the night at MSM, it's a real option for non-car visitors. You just have to lower your expectations for number of individual sites visited, if you don't have a car.

If you avoid driving in the larger cities, having a car is really easy. You'll be able to accomplish so much more than relying on public transportation. We picked up at CDG, stopped at Giverny on the way to Bayeux, where we stayed 3 nights in an VRBO in an excellent central location. Having a car also allowed us to take a private tour of the D-Day area in which our guide rode along with us and navigated, saving quite a bit over a chauffeured private tour. Highly recommend Chris: visitdday.com
If you're already going to be in Paris, take the train to wherever makes sense to pick up the car, drive around to your destinations, then return your car to a different location and take the train back to Paris. We drove from CDG because there is no direct train from there to Normandy and we didn't want to hassle with going into Paris and transferring.

FWIW, we were underwhelmed with Honfleur. It is a very lovely little ocean village, but it was packed with tourists. We went to the one site we wanted to see, had lunch and went back to Bayeux.

Do you have 4 full days, or is it 4 nights which really means 3 full days + transportation days? Makes a big difference in what you're able to fit in.

Hi
We did the Mont St Michel and the Dday site in two days.The D day sites will take up one of your days and the Mont St Michel a second.We stayed in the Centre of both at www.manoirdeherouville.com a few weeks ago and it was positioned perfectly for both and on the way back to Paris for Rouen and Giverny.We also took the tour guide from the Manoir and cannot recommend more.
The guide gave my wife and I a personnel tour of all of the sites,some on the route and some off the beaten track for the same cost that you would take on a shuttle bus from Bayeux and would not recommend to you if you are looking for a good memory.
Maybe contact Catherine at Le Manoir and she could point you in the right direction as she was brilliant with us for our planning while we were there.
Here is the email we contacted her on manoirdeherouville@gmail.com and she speaks perfect English.Tell her Rocky sent you and says Hello :-)

If you stay 2 days in Bayeux you can the first day do a full D-Day tour ( many possibilities ) and the second one go to Mont St Michel in the morning in a van (like the Churchill or Bayeux shuttle one), and coming back see the tapestry before doing at 5pm a City tour with Bayeux Discovery Walks. Then you can get the 8.09pm train arriving in Paris at 10.26. For the 3 other towns I don't know how to manage to see the 3 of them by train....

We followed the recs of many and stayed one night on Mont St Michel, and two nights in Bayeux for DDay sites, and one night in Les Andelys before hitting Giverny, but with a rental car. Easy driving for me, just a lot of tolls if you use the highways.

I would suggest dropping Mont St. Michel or making peace with not having enough time to see much of Normandy. It's a very large region. To give you an idea, we spent 7 days in Normandy in 2015, and our sightseeing schedule was rather well-planned. Even with that, we elected to drop Mont St. Michel to be able to see all the beaches, historic towns, and spend time in the wonderful museums.

Two days/three nights of our time were spent in the Honfleur/Etretat area. I can't imagine trying to navigate that area without a car. I would highly recommend renting a car for anywhere you decide to go in Normandy; it's an agricultural area and having a car will allow a significant amount of flexibility in terms of sightseeing.

Whatever you decide, enjoy!

Two friends and myself spent a memorable 2 days/3 nights with Sharon and Eddie from http://www.normandy-battlefields.com/
What a great experience. We came to visit Juno Beach and they made the experience unforgettable. Eddie has an in-depth knowledge of D-Day that makes you really appreciate the sacrifice made by so many.

But I'm getting ahead of myself. We arrived at their beautiful, yet comfortable chateau just prior to dinner. We were greeted with afternoon tea and shown to our rooms. Each room in the chateau has a theme and are extremely large with their own en-suite bathroom. Dinners with Eddie and Sharon and the rest of the guests are a blast...the meals are wonderful and the first night you are served from the bar...your second night you are expected to help yourself :)
On our second day of the visit we accompanied Sharon to Mont St Michel...an amazing UNESCO World Heritage site. It was a treat to be taken around by Sharon who has a real enthusiasm for architecture...and without her I feel I would have gotten lost!
If you are thinking about spending a few days in Normandy or exploring D-Day (whether it be Canadian, British or American themed) I wouldn't hesitate to recommend CDB Tours. If you start to add up the cost of accommodations, entrance fees, meals, etc., etc., you'll see that going with CDB is worth the price and the experience that both Sharon and Eddie bring.
If I find myself in Normandy again I will be making a stop at Chateau de Beaulieu!

Sorry to have missed a chance to provide help, but for anyone else looking to travel to the invasion sites of Normandy, we could not recommend more highly Eddie and Sharon Parks of CDB Tours, www.normandy-battlefields.com. They are a wonderful couple who host overnight(s) or just for a day tour. Eddie's knowlege coupled with his preparation is unrivaled by any guide we have used in the past. Sharon hospitality measures up to the finest qualities of a hostess. The site visits with Eddie's unique perspective as a retired military officer brings the magnificience of the sacrifices made by the greatest generation home as only one who has himself served in combat. Thank you Eddie and Sharon again, for the wonderful time spent with you and your service and sacrfices to our freedom. Dale and Sharon Allen, San Francisco Ca.

We did 5 nights -- one at Mont St. Michel, two in Bayeux with the full day a tour of the beaches and then two days in Honfleur with the full day Etretat. I'd do Giverny as a day trip from Paris which is what we did; we did Rouen that way too. But of course you fit in the things that interest you:
https://janettravels.wordpress.com/category/normandy/
We rented a car in Caen. If you can, a car is very convenient for this area. But if not then you will want to stay in towns with good transport connections. You can't 'base' if you have to take public transport in rural France.