It is surprisingly hard to rent decent bicycles in France. There are places that will ship by rail for a fee--for example Borgougne Randonees in Beaune (the outfit that Rick recommends in Burgundy) will do this, or at any rate used to. They'll deliver to a local hotel or bike shop.
Another place that I have had good experience with is Escapade Gourmand, also in Burgundy. I have heard of a similar place in Provence but have no personal experience with them.
The drawback, of course, other than the fee for delivery, is that you won't see the bike until you get it and you'll have to make any adjustments on your own.
I wonder about the hard sell you are getting from touring companies. Are these French? You might do better searching for a local equivalent of the above Bugundian bike renters. You could try to locate some local bicycle shops and ask them who rents decent machines.
If you find anything, post it here--I'd like to know. Good luck!