If they do then legally they are not allowed to call them Poulet de Bresse as the name is protected by French and European law. I don't know if the names of the 3 varieties can be used (Beny, Bourg, Louhans), may sometimes be sold under the name Gauloise in the UK.
It is very rare that any live birds leave France, though a breeding flock was exported to the USA in the 1980's and go by the name Blue Foot.