Paris and environs

Lucky granddaughter! I recommend reading a guidebook, perhaps RS France or Paris, to get some ideas. You can get it from the library but it isn't usually the most up to date version.

Rick's Paris book covers several easy side-trips, including Chartres (for the cathedral) and several nearby chateaux. Some people also daytrip to the D-Day beaches in Normandy (train travel 2 - 2.5 hours each way), but you could see more, including the Bayeux Tapestry of 1066, if you stayed overnight. Rouen (1.5 hours by train) is another possible side trip that only gets one paragraph in the Paris book but is well covered in the France book. Your granddaughter might get some ideas by watching Rick's videos online, if she has not yet seen them.

Versailles, Giverny (Monet's house and gardens), and Chartres (amazing cathedral) would be my recommendations. What a great adventure for you and your granddaughter!

Normandy would be a good multi-day trip, but better with a car, which you could pick up in, say, Rouen.

Ina Caro's Paris to the Past describes various day trips to historic and beautiful places, you might want to take a look for ideas. Or, better, let your lucky granddaughter browse through it and see what appeals to her.

You might check out Fat Tire Bike Tours in Paris..they also offer tours beyond the city. We did a tour last year to Normandy with them and it was fantastic...just get good directions from the train station in Bayeux to the meeting place.
Also, I have heard linkparis.com has outstanding tours.
What a sweet gift!

There are literally dozens of great day trips from Paris within an hour by train.

One thing I would try to do is pick some things their friends and relatives will not have done. One of my favorites is St. Denis the oldest Gothic church in Europe and the burial spot of French Kings (well until their bones were trashed during the revolution) Some wise soul managed to declare the tombs 'artistic treasures' during the revolution and prevented their destruction. It is a wonderful place.

You can see this and other recent day trips including Vaux le Vicomte (terrific) in my photo journal here:
http://janettravels.wordpress.com/category/day-trips-from-paris/

Malmaison, Josephine's place is also interesting and little visited. The town of Auvers sur Oise where Van Gogh spent his final weeks is interesting. Rouen is an easy day trip and the historic center is very different from Paris and very compact and manageable in a day trip.

I am a big fan of Moret sur Loing and Crecy la Chapelle for smaller towns with more of a countryside feel.

I'd be inclined to rent a place in Paris and then do some day trips. But if you do want a 3 day side trip to Alsace or Burgundy or wherever, put that at the front end of the trip so you are not racing back to Paris your last full day to catch the plane home.