Taming in the Copious Dogs Mod is very similar to the way wolfs are tamed, the biggest difference is that you use a dog biscuit instead of a bone. Once the dog is tamed it will not follow you directly. You have to give it a collar, and after that, use a leash on it.
For breeding to be done between two french bulldogs, they have to be 10 blocks near a heat source (fire or torch, not lava). They do not, however have to be near the same heat source. The french bulldogs must have a distance smaller than 15 blocks between them. When the requirements are met, just feed them both a cookie and let the magic happen.
When a french bulldog loses health, you can not feed it directly. You have to place down a dog dish and fill it. When there is enough food in a nearby dog dish, the french bulldog will come over and start eating. The french bulldog only eats if there are enough food in a dog dish to heal it completely.