Car or Train - Which is the more practical method of transportation in Normandy?
 

Plan on seeing D-Day beaches, small towns, Giverny, etc. after coming from Paris and returning back for flight home. Any suggestions?

Car is much much more useful for these types of places, even though they can be done by public transport.

Hands down, a car. There are SO many charming things to see on the back roads.
Since you say "coming from Paris and returning home" I would put the Normandy trip on the front end of your time. You get the car, do Normandy, return the car and then go to Paris. No driving in Paris.

The trip is already planned to have us beginning with Paris. I figured we could pick up the car the day we left the city and return it when we arrive back. Can anyone recommend some good (and cheap) car rental companies? Also, what are the policies for American drivers in France?

One alternative to driving all the way out to Normandy and back would be to take the train and hire a driver/guide at the Tourist Information Center. The car with guide will not cost significantly more than renting a car and driving yourself. These folks are highly knowledgeable about the battle, and the fact that their families lived through the liberation gives them unique insights into the period that aren't in history books.

1. First train from Paris to Caen
2. Visit the Peace Museum
3. Hire a driver
4. See beaches, cemeteries, museums
5. If time permits, see Bayeux Tapestry
6. Last train from Bayeux to Paris

- OR -

Instead of a driver, buy the Holt's guide book and get a bus pass from http://www.busverts.fr

I guess the easiest thing to do is to go to CDG and rent the car there and return there. There aren't any trains to CDG from Normandy so you would have to go back into Paris.
I find Robespierre's post about it "hardly being more expensive to hire a driver" to be surely disingenuous. Get the Michelin Green guide to Normandy for some lovely ideas for drives PLUS the D-Day routes. There is the Abbaye Road out of Rouen that is along a string of Norman churches. You don't say how long you are planning for this part of your trip.