I'm arriving in Paris on Monday morning and would like to jump on a train to spend a couple of consecutive days outside the city. Preferably, we would like to visit a place with plenty to do and see in a concentrated area, as we do not wish to rent a car. Ideas?

There is Reims, which is in Champagne region, where there's some points of interests and several champagne houses to visit. This can easily be a day trip from Paris, but if you just want to relax and take your time.

Is there a particular reason you don't want to rent a car? I see other posts of yours. Renting as soon as you arrive at CDG and striking out for Rouen for a first night is easy, for example.
For this question you might like to choose a destination that has service leaving from CDG such as Avignon. But once in Provence, there is so much to do that benefits from touring in a car.
Maybe Lyon has service from CDG. How long will you be in Paris?

Thanks for the responses. I am not completely opposed to renting a car, but since we'll have such a limited time in whatever place outside Paris we choose, it just seems like it would be possible to find a desirable side trip where we could cover everything on foot. Saves money and the car-rental hassle (I've had some bad experiences!). We only have 5 days in Paris if we do a two-day side trip.

You could take the TGV to Tours and spend a night. Tours has a nice 'vieux ville', museums, and you could book a van tour of some chateaux, if you liked.

Trains
www.sncf.com

Tourist Office
http://www.ligeris.com/index_us.html

Chateau/Loire tour (transportation only)
http://www.ligeris.com/usa/bus_acco.html

Reims/Epernay for champagne.
Beaune for burgundy.
Avignon/Aix for Cote du Rhone wines, how about a nice Chateauneuf-du-Pape.
Wow...It's your choice. All easy by train.

Or TGV to Angers (1.5 hours); there is plenty to do and see in this beautiful, pleasant city with a mild climate--castle, extensive medieval quarter, free wine tasting center, very attractive parks, wonderful inexpensive restaurants (about 15 euros or less pp for three course lunch WITH wine and coffee), friendly people.
Avignon is about as far as I'd go. But with only two days, I'd limit my train ride to 2 hours max each way, preferably with no changes.
I can understand how you'd prefer not to rent a car...much more relaxing to settle yourself in the train, open a bottle of wine, and admire the view.

Honfleur in Normandy for charming streets, half-timber houses and a breathtaking 17th-century harbor, museums (four), restaurants (dozens), art galleries (ditto), antique and regional food shops, and even a beach, though most people don't know it's there.

Or one day in Dijon and one in Beaune.

Just spend all your 7 days in Paris. That is not really that long (or long enough). If you want a day trip, take a train somewhere. As for the expense of a car, it is more about the convenience and not eating up your time waiting for trains, or fitting their schedules, especially for a 2 day trip.

Plus the time it takes to find your hotel and move in and out of it.