sig, in Canada for example, wines produced with the champanoise method are labeled "Sparkling wine, champanoise method".
I'm no expert, but from what I understand, in wine making, there are many conditions. There is the variety of grapes itself, the recipe used and the actual region where it's produced. And the year it was made. The region it's produced is important for certain wines because that region has specific conditions that are not present somewhere else, such as the soil, the sun conditions, the amount of rain, etc. That is also the reason why for specific wines (not all wines), the year is also important; certain years get more sun, more rain, etc. For that reason, a true Champagne is only produced in the Champagne region, and so is the Bordeaux wines. Although wines made with the same variety of grapes, using the same recipe (or method) can actually make wines equivalent, or event sometimes superior to the ones actually made in Champagne or Bordeaux, they can't be called as such because they did not get the exact conditions as those wines produced in those regions.
But there are other wine that are known by their method or their grapes, not at all specific to a region. It's the case for example of the Cabernet Sauvignon, which is a variety of grape, not a region.