The first thing you need to know is that the SNCF (French national railroad) has made it much more difficult in the past few years to take bikes on trains, especially the TGV trains. Therefore don't assume you can easily get from southern France back to Paris with your bike on the train. On many/most regional trains, you can often still take a bike, but the rules vary by train. On some, you load it yourself and it's free. On others, you have to pay. And on others, no bikes allowed. You have to check the schedule and the specific train.

You wrote that you're going "in a few weeks", so I'm presuming that means August. In tourist areas, it will be crowded. In the Rhone valley and Provence, it will be hot and Provence will be crowded.

Although my absolute favorite region for touring is in Perigord in the Dordogne & Lot valleys in SW France, it probably makes sense for you to stay in the northern half of France if you only have 2 weeks. The Loire valley has a concentrations of quiet roads, bike paths, and sights to see. Burgundy has a good network of bike trails (paved & unpaved) and nice scenery. Normandy and Brittany are both nice, too. I would not, however, recommend riding between Calais & Paris. It has boring scenery. The same goes for the area due north of Paris.

If you think you'll be staying longer than 2 weeks, then I would suggest including the Dordogne & Lot valleys in your itinerary.