You can legally make a a product with the same method. For example, sparkling wine using the same method as champagne.
But it it is not made in the right region, it can not be sold under that region label. Champagne needs also the correct grapes from the Champagne, so the sparkling wine after the champagne method should never to be called champagne.
Similarly, a tea may be processed just the same as Darjeeling Tea, but it can't be called Darjeeling in trade if it is not from the right region.
Most countries that have marks for geographic origin respect them globally.