Historically it would have been still, but there's no reason not to be able to apply carbonation methods that've been found to carbonate grape wines.
Methode champenoise is a relatively new concept, yet as with grape wines it seems that its dry, relatively high alcohol types that are best suited.
Plus you need to think on method as well as materials for safety. Then there's the additional processing kit required.
After all, its relatively straight forward to produce something that can be force carbonated before being chilled down and bottled, but that gives you largish bubbles like pop/soda and it really needs proper champagne type carbonation to achieve the tiny bubbles that you see in that type of sparkling wines......
Methode champenoise ain't as easy as it sounds......