Did I miss something? Why would you do this aside from creating meat mutts?
Am Bresse have some great, very serious breeders out there now doing fantastic work. Pick a line and develop your own line from that, a few years down the road if you discover there is a fault or defect you cannot correct (physical, health, etc) there are multiple other genetically distinct lines you could turn to.
On the flip side, if everyone just starts mixing all the bloodlines willy nilly, you get a mess that's homogenized over the ENTIRE available population instead of genetically distinct bloodlines. This is one of the biggest problems rare breeds face... a lack of serious breeders putting in serious work on THEIR own pure strain allowing multiple genetically distinct flocks to co-exist independently "as back up" in case one hits a bottleneck and needs a single bird brought in to correct a problem.
You don't save a breed by outcrossing it to literally everything else out there.
You don't save a breed by reproducing and selling as many low quality birds as you can.
You save a breed by devoting your resources and time and energy to it and hatching and growing out as many as possible every year and then putting the bottom 80-90% of them in the freezer and starting over again the next year until you've bred out defects and faults and improved vigor and type and then, maybe, you can share some juvenile pairs or trios (not eggs or chicks) with someone else you think will have the gumption to do the same thing.
THAT is how you "save" a breed. It is a singular dedication, not a chick factory collection.