Transportation from Paris to sights around Normandy

I think I may have answered your Brussels question earlier... Anyway, if by "Normandy" you mean sites associated with the DDay invasion, the best method would be either by an organized tour ( I believe the most popular one on this website operates out of Bayeaux) or by rental car. The sites sit spread out over a fairly large area and difficult to link together by public transportation. Don't try it as a daytrip from Paris either.

Take the train to Bayeuax or Caen, rent a car, spend the night.

To save money, rent the car in Paris and drive from there.

I rented at CDG and just followed the GPS as well as directions from Ed on this website (hopefully he'll chime in) but it was really easy and having the car to drive around as we pleased was perfect. We stayed in Bayeaux and loved it there. Then just returned the car to CDG and took the train into Paris.... really easy...just pay attention to the signs but with 5 people you should not have a problem.

I don't know if your family of 5 includes children or whether they get a discount on the train or not but if you are all adults you might want to look into hiring a car service between Bayeux and Paris. It is expensive but if you divide it 5 ways it might not be much more than 5 train tickets particularly if you need taxis to the train stations and you'll be picked up at your Paris hotel or the airport as a bonus. You would then have to either rent a car in Normandy or use one of the tour companies. We plan to do that in September with four adults. The company we are going to use between Bayeux and Paris is Albion Voyages. It was recommended to us by a couple of places but we haven't used them yet so can't give a personal okay. If you are traveling after October we'll know then how they did. Also the Hotel Churchill in Bayeux has a shuttle to Mont. St. Michel you could use.

We took the train to Caen and picked up our reserved rental car right across the street from the Caen RR station. We had a GPS with European maps so we took off for Bayeux,about 15 miles, and had preprogrammed the address of our hotel into the GPS. Easy peasy. We met the D Day tour the next morning right behind the Churchill Hotel and off we went. Like many tours we wanted to spend more time at some places so we used our rental car and returned the next day and spent 5 hours at the big American cemetery above Omaha Beach. Very moving.... We actually stayed at a rural B&B about 15 miles east of Bayeux so went off to MSM the next day. Check out bandbnormandie.com for the rural farm. My advice, get a rental car which gives you the freedom to stay where you want and go where you want, when you want.