I have not tasted Bresse, but I know that part of the reason for the rave reviews is that the Bresse are tender due to having very short muscle fibers, similar to the Crevecoeurs I raise.
I have also read that in France there is an elaborate process for raising Bresse that contributes to their flavor. In France, the breeder must guarantee at least 10 square meters (to me, a meter is a little more than a yard) of "bocage," a designated mixture of woodland and pastureland. The breeder also feeds a combination of corn and wheat and milk from their first month onward, and the birds must also be allowed to graze on grass, worms, seeds and insects to complement their diet.
To me this sounds pretty much like free-range, in parts. I guess the milk might be easy for a dairy farmer, but I don't think I will be feeding my birds milk any time soon, mostly due to the price.
The other part of the flavor package, I suspect, is that the Bresse become meat at a later age than most American chickens. American chicken is pretty young when it gets to the slaughterhouse to become our food--think "veal"--tender, but less flavor than beef. Bresse is harvested at a later age, and has a chance to develop real chicken flavor, but with lots of steps between, including pasture and special diet, and a genetic predisposition to short muscle fiber, to keep the meat tender, even at a more advanced age.