Grandmother and two Granddaughters in June

What a wonderful trip for you two and your Grandmother. I would think a week to ten days in Paris. You could plan one day trip to Versailles. And you could consider and plan more on spur of the moment another day trip depending on how you are all feeling, the weather, etc. Paris is wonderful to just "be". So don't short change it. I would get an apartment so that you have a nice common area to share for a break between site seeing, you don't always have to eat out in a restaurant, etc.

How much time do you have? You can spend a month in Paris without any problems. How many days to you want to spend on the side trip? You don't have to stay in France, there are fast trains that take you to the UK, Belgium, the Netherlands, Germany or Switzerland in a few hours. But if you are looking to stay in France, Normandie is not a bad option and you can also consider Bordeaux or Strasbourg.

We have 2-3 weeks, depending on flights. I have been to Bordeaux before when I went to Spain, but Germany or Belgium could be interesting. I would say the side trip would be 2-5 days, depending on where we go. I want to allow a could of days in Paris for recovery before we even try to see anything.

...Would we be able to take the train to and from Versailles, and see it well, all in a day? Or is it worth moving and staying in Versailles?...

Yes, you can do it by train in a day. No need to relocate.

Another day trip to consider is Reims. No need to relocate, and you can get there quickly by train. It has a very historic cathedral, the Museum of the Surrender (WWII). and some champange houses to visit.

Of course if you decide to leave France, there is the high speed chunnel train to London.

All I can say is what a gift you and your cousin are giving your grandmother — and yourselves. This is really beautiful, and the memories you make will be there all your lives!!! And you are making your grandmother feel so treasured.

Agreed that you can get to Versailles on the train without moving there. I also agree that Reims would be a lovely side trip — the World War II connection with the Surrender Museum with its cool map room, and a visit to a Champagne house or two !

Note that the government has instituted a fixed-rate tariff for taxis to and from the airports. Assuming that you are flying in and out of Charles de Gaulle and all arrive and depart together, the fixed rate if your hotel is on the Left Bank is 65€, or €56 to the Right Bank (and in the reverse directions when you leave). That rate covers all three of you and your luggage with no extra fees per suitcase or anything like that.

abbylynm,
With 2 weeks I would stay in Paris. With 3 weeks, I might head to the Alsace region (Strasbourg/Colmar, maybe a couple of nearby German cities...Metz?), a 2-3 hour train ride from Gare de l'Est. Search in this France section of the forum for suggestions about Colmar and Strasbourg for ideas.
Also, I concur with a day trip to Reims, and Versailles. Just be sure to give yourselves plenty of time in Paris, especially with going slow. Hubby and I are 81 and 82 now, last in Paris at 79 and 80, and could easily do two major sights a day with a relaxed lunch in between and a short evening stroll or vedette ride. One day could be the Eiffel Tower (from below) and along the Champs de Mar, walk to the Invalides (Army Museum/Napoleon's tomb), then a comfortable sit-down lunch to rest and relax. Follow lunch with a not very long walk to the Rodin Museum and Gardens. Fabulous sculptures in the gardens! And several places to sit and enoy them. Even if you don't go inside, it is worth it.
Versailles will be an all day trip, but not a long train ride there and back. I believe there are carts of a sort to rent to visit the Petit Trianon and the Grand Trianon and the Hameau. Otherwise they are a long hike through the grounds from the palace and fountains. Reims is also a good idea for a day trip...the cathedral where nearly every French king was crowned and which has beautiful stained glass, the WWII surrender museum site, and champagne!
As someone older than your Grandmother, and not a hiker or bicyclist or excerciser, two artificial knees and a somewhat wonky back, I am sure your trip will go very well. Don't shortchange Paris! Try to attend a concert or performance somewhere, whether at Ste. Chapelle, the Opera Garnier, or any one of a number of churches or theaters. Take frequent breaks if tired (coffee, ice cream, patisseries, wine), and use a taxi if you don't feel like walking any more or if the metro seems too intimidating (long steep stairs, crowds, confusing platform directions). When I am tired of walking, I find a place to sit and just look at Paris and Parisians and relish the fact that I am IN PARIS! I could easily spend three weeks there, but understand your desire to see someplace else as well. But do try to give Paris two weeks. It is more than Notre Dame, the Louvre and the Eiffel Tower. (It took me seven trips to Paris to finally see the Cluny Museum, and I love the Rodin Museum so much I go with every visit. I still have a list of things and places I haven't seen.)
Amusez-vous bien!

Forgot another good day trip from Paris.....Chartres!