I am looking for some help finalizing an itinerary for our trip that is one month away. I have booked our flights which are in and out of Paris. I haven't booked anything else yet. I had thought about Paris for 4 days at the beginning and then maybe a few days in Normandy and Mont St. Michel and then ??? I had wanted to go the South of France but don't want to sacrifice a whole day to travel. I will book flights differently on future trips for sure. I am overwhelmed with all of the things to see and I know that we will not see them all. I wanted to be back in Paris for our last night on the 15th. Any suggestions are most appreciated. I do not plan on renting a car and really want to be able to incorporate some train travel as it would be such a fun experience for both of us. I will be doing some organized day tours as well...Versailles and Giverny, a tour of the Louvre and a tour in Normandy.
There are unlimited good options in France, which makes trip-planning quite difficult if you're trying for "the very best". Shoot instead for "a lot of fun".
I don't know anything about your interests or your daughter's beyond the clues provided in your post, so these are just some random thoughts:
Four nights is no time at all in Paris if you're going to spend a chunk of a day going to Giverny and a chunk of another day going to Versailles.
Normandy is nice in the summer, but you might be quite unlucky with the weather there in April.
You may be too late to get a good rail fare (or a budget flight), but you might be able to get all the way to southern France (Nice, Avignon, etc.) on your arrival day, assuming you're scheduled to arrive at CDG in the morning. That first day is pretty non-productive anyway, because of sleep-deprivation and jetlag, so spending it to get to one of your other destinations is often a very good use of your time. It would make for a very long day, however. (If not southern France, consider heading to Normandy; Bayeux's 3 to 3-1/2 hours from CDG by train.)
There are some very good one-day van tours of the D-Day beaches. Two companies often recommended are Overlord Tours and Dale Booth. Most of their trips depart from Bayeux.
You're right about being back in Paris the night before you fly home. That's why a lot of people prefer to end their trips at the departure point, rather than visiting that city at the beginning of the trip. Going straight to one of your other destinations means you don't have to check into Paris hotels twice, which makes for some additional sightseeing time.
There's so much to do in and around Paris, I wouldn't feel bad about sticking with Paris and day trips for the limited amount of time you have. Versailles can be a full day if you really delve into it and go all around the gardens, or it can be more like a half day. Giverny is further out, but it has fast train service so again you can do it easily as a day trip.
If you do want to spend a few of your nights in Normandy and also visit Mont St. Michel, be aware that the weather in early April is likely to be chilly and wet. Frankly I wouldn't want to go there without a rental car because the public transportation options are very limited. Other travelers may say otherwise.
Heading south from Paris by train you could spend 3-4 nights in the Loire Valley (Amboise is a popular base) and take one or more van tours to visit chateaux, if your 11-year-old would find that interesting. Or you could experience high-speed rail with a TGV trip to a destination that appeals to you. For TGV routes, see https://www.tripsavvy.com/tgv-train-route-map-france-1517930
Is there a particular reason you're interested in Normandy? That might change my suggestions....
We just took our 11 year old to France last year, though in the SW. The things she was most impressed by were the tiny medieval villages, climbing around castles, and being able to have some freedom to run around the streets (with us, of course, but she liked running a few feet ahead and feeling independent :) )
With that in mind, like the above commenter, I might switch focus to Paris and the Loire. Actually, I'm taking 3 teens to France this summer and those are where we're focusing because I think it will be the best version of France to show them on a first trip! In the Loire, you get impressive castles and smaller towns that will be approachable for a kid and let them feel more comfortable. Since you don't want to rent a car, I'd suggest basing yourself in the Loire for 3-4 days and then back in Paris. However, I also think you could easily stay in Paris the whole 10 days and do a few day trips. You could certainly spend a full 10 days in Paris and barely scratch the surface, but there are also lots of places you can get easily via train in about 90 minutes or less, and it might be less stressful than moving around. Reims, Rouen, Dijon, Angers are some suggestions for smaller towns that make great day visits and would show something different than Paris. The train tickets should be fairly cheap and could even be booked the day before (allowing you to be spontaneous or let the weather dictate your days). Plus if you know you're sleeping in the same place every night, it makes it easier to plan for dinner or just relax at the end of a day. It also makes an apartment rental more feasible--great if you want to be able to cook.
For Paris, try to carve out time for La Villette and in general time to play on playgrounds. Our 11 year old loved how different they were from what she's used to, and she was able to "make friends" and play with French kids despite the language barrier :)
Oh, and if you want to do Giverny, rather than an organized day trip, book a train to Vernon and bike the rest of the way! You'll see several bike rental places outside the train station, and it's a pleasant (fairly) well-marked ride to Giverny. Check the weather first though--it's not unusual for it to rain in Giverny or Paris but not the other.