YOu might check out Auxerre

Dijon? Nancy?

Beaune or Dijon in Burgundy

www.beaune.com best for food wine scenic capital of Burgundy

Another vote for Dijon. Only 1h40 from Paris. You can walk everywhere in the historic centre (no need of a bike to go shopping)and you can also rent bikes to explore it. http://www.youtube.com/watch?v=w5CojSGoJ4k (TO video)

Here are a few ideas http://www.cotedor-tourisme.com/bourgogne-leisure-activities-and-events---visits---heritage_en_04.html#
You may also go to Beaune (by train or bus)and rent bikes near the train station to discover the wine coast. http://www.route-des-grands-crus-de-bourgogne.com/Affiche.jpg

All good suggestions. www.burgundyeye.com Normandy in the town of Bayeux would also be a good destination and might be a 2-3 hour ride. http://en.wikipedia.org/wiki/Bayeux Honfleur would also be a good destination. http://en.wikipedia.org/wiki/Honfleur

Neither Dijon or Nancy are remotely small towns, though. So they won't work if that is really what you want. Beaune would be a good idea as I think it fits the desires better.

Or you could go to some small town in the Loire as the Loire is pretty flat and good for cycling around to see chateaux, if that appeals. Blois might be one idea. I really liked Angers a lot, farther west, but it isn't super small, either. But there is a lot to see there.

By fast train, a lot of the country is within a 3 hr train ride, though, so it doesn't have to be close to Paris. Avignon is, for example and that's down in Provence (not that I think it's a small town, but just for the distance).

For something really different, you could go down to Le Puy-en-Velay in the Massif Central which does have mountains and is a small town. It's fairly direct on the train line from Paris, also (I"m sure probably one transfer), but I'm not sure if it's within 3 hrs.
see http://www.ot-lepuyenvelay.fr/

folks bicycling right on the front homepage of the tourism website. I think it is more like 20K population, but that's a lot smaller than large cities like Dijon or Nancy.

Delightful as they are, neither Dijon nor Nancy fit the description of a "small, country town" - which is what the OP asked for (repeatedly).
Closer to the OP's brief is Beaune or some of the Loire valley towns - Saumur or Loches, for example - and biking around the LV region is very popular.

On the topic of Burgundy, I have just written a trip report about visiting the countryside there that is full of photos and descriptions and could give you some excellent ideas for that region, including small towns, if it interests you. Here is the link to that report:

http://tinyurl.com/6dkeozh

This region is also great for biking. If Burgundy interests you then I and others can probably make further suggestions.

Your request is very general as within a 2-3 hour train trip from Paris there are hundreds (?thousands?) of towns/villages that meet your criteria. As a matter of fact, you wouldn't even have to go more than an hour by train from Paris to satisfy your desires. The rural countryside is much closer to Paris than many people are aware. Let me show you what I mean by giving a link to another of my trip reports where I ride my bike in the area around the medieval town of Laon, a bit over an hour by train north of Paris. Lots of pictures and descriptions here:

http://tinyurl.com/298tppr

I re-read your thread and I think I see more clearly what you want. It seems like you are into biking and I have extensively explored many regions by bike that lie more or less within an hour by train from Paris and I've got many trip reports (with pictures) about my bike trips. Here are links to a couple more of my bike trip reports:

Near Fontainebleau: http://tinyurl.com/4bduunh

Biking to Provins (walled medieval town):
http://tinyurl.com/253zs6r

Near Compiègne: http://tinyurl.com/334l4ao

Near Giverny: http://tinyurl.com/362xrle

I'm not suggesting you should stay in any of these places, although I bet you would enjoy any of them, but I'm illustrating the point that close to Paris there are endless possibilities and you'd probably be happy with any of them.

Sounds like Beaune would be perfect for you. If you are interested in an apartment we stayed in a lovely, newly restored one right in town with the boulangerie sp?) right down the street. It had 2 br. 1.5 baths, charming decor, washing machine. furnished with some antiques, wife of owner is Canadian so communicating not a problem.

Beaune has great food, wineries nearby, biking, small town... If we ever get back to that area this is where I would stay. If you want the name respond to this posting.

FMT, your trip report of Burgundy is just wonderful. You have such a good eye and hand for story telling and make it so interesting. I'm really enjoying this one (as I did your tome on the 12th arr) and now want to read the others that you've done. Is there a way to subscribe to your blog ?
(Apologies to the OP - I didn't mean to hijack your thread.)

Hi A,

Another vote for Auxerre.

Beaune is also nice, and easily accessed via Dijon.

Lyon isn't a small town but it is not touristy and rather interesting.

Enjoy your visit.

Hi Mathieu, thank you so much for your compliments. Actually I have not yet created a blog but I will soon. For now I post all of my reports on a proboards site that you can visit at www.anyportinastorm.proboards.com. Just look in the France and Paris forums and search my name and you'll find all of my reports there, as well as hundreds of other very interesting things.

Sorry to the OP and others for the interruption of the thread.

I suggest Avallon and you can visit the vineyards in the
area. Lots of nice places to stay.

Saumur would fit the bill, and it's reasonably flat!

You could try tours in the Loire Valley, easy 1 hr tgv ride from paris, for things to see and do try myweekin there's lot of lovely bistros and chateaus and cycling if in summer