Of course when just one region of one particular country has the ability to name a certain product, then that nation and that region has an advantage. It is probably a justified advantage, but provided that there is some sort of standardization across the board for the various products in its own category, such as wines.
France does benefit from exclusive rights to the brand name "Champagne." By owning the brand name, the country gets to make important decisions about international trade which, of course, they will choose to benefit their country. France is keeping the economic value of the product protected and higher because of the exclusive rights they have.