This isn’t entirely true, according the article. If a producer in the US was using the name “Champagne” before 2005, they can continue to do so, but producers can’t start using it anymore.

It took two decades of negotiations, but finally, in 2005, the U.S. and the EU reached an agreement. In exchange for easing trade restrictions on wine, the American government agreed that California Champagne, Chablis, Sherry and a half-dozen other ‘semi-generic’ names would no longer appear on domestic wine labels – that is unless a producer was already using one of those names.