The french bulldog is the third most popular dog in Australia 
Are they a large breed or a small breed?
They are a smaller breed. To Reduce their size, they were crossed with terriers while some were crossed pugs
Were they bred for a certain reason?
They were used for blood sports but they were outlawed in 1835 which left them unemployed. Since then they have been breed from a sporting breed to a companion breed. 
Is a French Bulldog registered with the AKC? I was thinking about possibly getting one, but want something recognized by the AKC?
French Bulldog
The French Bulldog is a breed of domestic dog. In the 1800s, they were the result of a cross between Toy Bulldogs imported from England and local ratters in Paris, France.
The breed is popular as a pet; in 2015, they were the fourth most popular registered dog in the United Kingdom, and in the U.S., the sixth most popular AKC-registered dog breed. They were rated the third most popular dog in Australia in 2017.
History.
The origin of the modern
use changed from a sporting breed to a companion breed. To reduce their size, some Bulldogs were crossed with terriers, ratter dogs from the "slums" of England. By 1850, the Toy Bulldog had become common in England and appeared in conformation shows when they began around 1860. These dogs weighed around , although classes were also available at dog shows for those who weighed under .
At the same time, lace workers from Nottingham, displaced by the Industrial Revolution, began to settle in Normandy, France. They