
Frenchies come in a variety of colors of which the Blue Frenchie is one. Frenchies with the blue coat color can be registered by the AKC but are not recognised as ‘breed standard’ so this color cannot compete as a show dog in competitions, unlike the other Frenchies.
The officially accepted coat colors for Frenchies are brindle, cream, fawn, fawn brindle and white or any combination of these colors; but not the blue coat.
It is sometimes called a ‘Rare Blue French Bulldog’ and the French Bulldog Club of America refers to it as a fad color or disqualification color. The FCBA strongly discourages the breeding of this coat color as they believe such breeders place more importance on breeding for color than considering the potential health issues.
Resource:
https://animalcorner.org/dog-breeds/blue-french-bulldog/