Outside Paris recommendations

Tough decision. They're both great for different reasons. Yes, Burgundy can be considered quintessentially French (over dinner, a Burgundian resident said Burgundy is "La France Profunde."). But the chateaux of the Loire and Dordogne are magnificent (and different -- Loire is pleasure palaces, while Dordogne is fortifications). For wine tasting I love the Loire (nothing too much in the Dordogne in that respect); lots of diversity and small producers. For biking, I would guess the Loire is better, because it's flatter. I think if you haven't been to any of those areas, I'd choose the Loire/Dordogne, if only for the magnificent chateaux. Our first 2 trips to France many years (not counting Paris) were the Loire and the Dordogne.

Just pick one, slow down and enjoy. I prefer Burgundy and have journeyed through several times and also spent a week in a cottage in Semur en Auxois and then drove around the area.
https://janettravels.wordpress.com/category/burgundy/
Loved Burgundy, but the Loire and the chateaux there are also lovely; we love the Dordogne best of all but again you can easily spend a week there. We spent a week in a cottage there this fall in a small village (Cadouin) and did so about 10 years ago. This is a wonderful region and the caves are magnificent. Visit Font du Gaume or Roffignac for the real deal and the Lascaux II recreation is also pretty amazing.

We have traveled to Burgundy several times. The northern section, Auxerre, St-Florentine, Chablis, etc and then east through Vezelay to Beaune, Dijon and the wine villages. It is a wonderful area to visit, historic sites and wineries, charming villages. It is easy to access from Paris by car or train,
You also mentioned Colmar but it is in Alsace, not Burgundy.

Thanks Robert, JanetTravels and Suki for your quick responses!

I'm leaning towards the Burgundy and Alsace region, since it includes so many small villages, and I love Beef bourguignon, escargot and pinot noir! :-)

Thanks!

I don't think you can go wrong here -- unless you try to see all three regions in a week. Save something for your next trip!

If you really have a full week, you can get a nice taste of two regions. Or relly dig int one. You could even manage the Loire and Burgundy, though it is a long drive.

Consider taking the train between Paris and these regions, unless you like to drive. The train is faster. Rent wheels once you arrive.

I had a wonderful time tootling around Burgundy (based in Avallon) and Alsace (based in Eguisheim), then dropped the car in Strasbourg for 2 more great days.