We breed both standard and rare colored frenchies.
A standard color is one that is allowed in the confirmation show ring, per the breed standard adopted by the French Bulldog Club of America.
The rare colors, by far the most popular, are registerable with the AKC, and can compete in all forms of AKC competition except for confirmation.
This is a political thing with the AKC, with no verified reason other than the breed standard.
Below you can see pictures of our dogs and puppies, and the colors we are able to produce.
The puppies and dogs above are all either our dogs, or puppies we have raised.
Our standard colors include brindle, fawn, brindle pied, fawn pied, and cream.
Our non standard colors are blue, blue pied, sable, black and tan, blue and tan.
Our merle pattern dogs can be gray with black, blue, fawn, or pied with any of the above mentioned colors.
We do have a pair of creams that we have not yet bred.
If you are interested in the genetics that go into breeding the various colors, there are plenty of web sites with charts and detailed explanations. Here is one that is pretty thorough without being too technical to understand.