I see renting a bike there as the better option. It's easy, not that expensive, and eliminates logistical planning. Packing your bike is expensive, forces you to collect baggage (when you normally only use a carry-on), and risks damage or loss.
Originally, I thought a good road bike made the most sense but my friend has rented the hybrid bikes (in Ireland) and was happy with them. He also said he got regular peddles for the rental so he could bring a regular pair of running shoes rather than a specialized bike shoe plus other shoes - which sounds like a good choice. As we get closer to the trip, I'll consult him more about the right mix of riding/rain gear to pack.
Even though I'd probably prefer the Dordogne. The Loire makes more sense for this trip. My friend is really interested in WWII history, so Normandie is a natural fit. The Loire also makes a handy circular route for flying in and out of CDG conveniently. I'll have to think more on how much time to spend in Paris and whether to spend most of it before or after the rest of the trip? The nice thing is Paris can add flexibility, we don't have to fly there or home together but can join up there for the rest of the trip - or have extra days there if one has to go home earlier.
I've also had interest from other friends about going, so I may end up organizing for a bigger group. I don't mind as long as people can keep up and don't complain (I do plan on limiting to about 40k a day, or less, of riding so it will be relatively easy). I'll probably commit to a solo trip, in case everyone bails out but build in flexibility for whatever size group it turns into. I haven't traveled with any of these people before so that, in itself, is an adventure. They're all outdoorsy hikers, bikers and campers so hopefully my itinerary will be a good fit.
So the rough itinerary as it's taking shape is Paris, Rouen by train, pick up rental car, Bayeux, Mt.St.Michel, Rennes, Saint Nazaire pick up bikes, then something along the general route of Nantes, Angers, Tours, Blois, and Orleans, drop bikes, train to Chartres for a day stop then back into Paris.
I need a lot of fine tuning on the bike part of the trip along the Loire. If anyone has sights, lodging, dining, or even entertainment venues they really enjoyed in the area please post them.