Nope! Just like all bourbon is whiskey but not all whiskey is bourbon, real deal Champagne can only come from Champagne, France.
Sparkling wine is made in a variety of ways. The Italians prefer the Charmat process, where the wine undergoes secondary fermentation (resulting in carbonation) in steel tanks. Popular, inexpensive brands prefer gas injection to get their bubbles.
The traditional method invented in France is a strictly regulated, extensive process. You’ll still occasionally see labels claiming to be “American Champagne” but this is technically impossible. The laws in the United States and elsewhere have been changing to preserve the integrity of regional processes and reputation, but there are still a handful of long-lived brands allowed to market themselves as something they are not.