Been to France a bunch of times and am taking two of the grandchildren there this summer.
Here are my suggestions:
Go to Mont St-Michel. It is a unique place. I have been twice and would return again.
The Memorial de Caen is a museum of peace and war in Caen and is a fascinating place.
I found the town of Rouen, along the Seine and on the way to Paris, to be fascinating. It's where Jeanne d'Arc was burned at the stake -- the greatest public relations disaster in English history -- the French still remember almost 600 years later. It's also where Julia Child had her first meal in France circa 1947. Interesting cathedral and some good places to eat.
Giverny, where Monet lived and painted, is also on the way to Paris. His sizable home and studio is open, although the lily ponds are more interesting than the exhibits. If you really want to see Monet, go to the Orangerie off the Place de la Concorde.
Consider getting a guide for Notre Dame and the Roman excavations on the plaza there. The Ile de la Cite has been settled for 2,000 years. The premier place to visit is Ste. Chapelle, a perfect gem of a Gothic chapel that was consecrated in 1248 -- uhhh, a while ago.
I always use le Metro when I am in Paris and have never had any problems, except that some of the routes and stations are complicated.
You may want a guide for the Eiffel Tower -- ask at your hotel -- because a guide can get you to the front of the line, which is a real advantage. Our guide also showed us the basement below the tower, where all the cables and elevator mechanisms can be seen.
You can walk all over "old Paris" and cover a huge amount of ground in 45-60 minutes. This is a walking city, much like London and Manhattan.
The neighborhood restaurants tend to be clustered along side streets. For example, the Japanese restaurants near the Palais du Luxembourg. This is especially tru in neighborheeds in the 1st and 2nd district (arrondissement).
Sacre Couer and Montmartre are up in the heights --there is a funicular -- visits should be combined, although this is a touristy area these days.
Anyway, bon voyage!
Sage Grouse
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'When I got on the bus for my first road game at Duke, I saw that every player was carrying textbooks or laptops. I coached in the SEC for 25 years, and I had never seen that before, not even once.' - David Cutcliffe to Duke alumni in Washington, DC, June 2013