I guess it's "generic" in the sense that everyone calls a sparkling wine "champagne", same as everyone calls a copier a "Xerox machine", but if some other company would try to sell their copier using the Xerox name, they would still be sued by Xerox (the company)?
At least here in Europe, even children know that “sparkling wine” and “champagne” refer to different things.
There is a kinder variant for such - prosecco, which can actually mean OK quality (within sparkling stuff bounds, which are not high).
But yeah calling anything Champagne apart from stuff coming from Champagne is a bad form and looked down upon a bit. Small kids do such mistakes and thats fine, adults shouldn't.
Not all adults care about the origin location nor should they.
If you’re ordering “sparkling wine”, you are not going to get a wine made using the méthode traditionnelle.
You will get an entirely different style of wine.
The origin location is really secondary. “Franciacorta” gets you something like Champagne, “sparkling wine” does not.