Not exactly. The Bouvier des Flandres is the Belgian rough-coated, cattle-herder originating in southwest Flanders and on the French northern plain. Whereas, the Briard is one of several sheep-herding dogs from France, the others being the Beger Picard, Beauceron, and Pyrenean. The Briard is the large goat-haired variety, while the Beauceron is the smooth version. Both Briard and Beauceron have double dewclaws on the rear legs. The Pyrenean Sheepdog is the small hairy type, with the Smooth-faced Pyrenean Sheepdog less hairy, but not completely smooth-coated.
As for the Briard and the Bouvier, both are bearded herders from a similar part of Europe. Both are considered "head" breeds as there is considerable description of the head in both standards. Both are shown with either cropped or natural ears. The Briard topline is constructed with a very slight incline, downward from the prominent withers to the back which is straight, to the broad loin and the croup which is slightly inclined. The Bouvier must have a firm level topline. The briard tail is uncut, whereas the Bouvier tail is docked. While the Briard must have double dewclaws on the rear legs, if the Bouvier is born with any dewclaws, they are to be removed.
Additional similarities and differences can be found in the breed standards on the AKC website. Several articles comparing the breeds are available from the Briard Club of America .