We are arriving in Paris but are wondering if we should rent a car there or take a train to Alsace region and rent car there. Any suggestions?
If you're going to get a car anyway, you might just as well drive instead of slowing down the whole trip for another change in mode of transportation. Strasborg is only about three hundred miles (four and half hours) from either Paris airport and there's a good bit to see along the way.
If you rent in Alsace, you will likely get to Alsace faster, and you may be able to save a rental day if you sightsee locally the first day you are there. These benefits are small and whether or not they outweigh the benefits of having a car during the trip probably depends on your own attitudes about driving.
Take the TGV out and then rent the car.
You will save your nerves and save a fair chunk of time too, IMO.
I assume you're going to stay in Paris first after the long flight, which is what I would do, at least for a day or two. Then from Paris Est-Strasbourg take the TGV, which is 2 and 1/4 hrs. or so. I did this as a day trip in 2009, hadn't seen Strasbourg in ten years. You can rent the car there.
Peg, Depending on time, I would rent a car at CDG and drive. On your way, spend some time visiting the American WW I cemeteries between Paris and Reims. Visit the cathedral in Reims. Continuing west, consider stopping in Verdun. Make your way to Metz to see its beautiful cathedral as well. The distance is not great and you'll get a good feel for the countryside! Have fun!