If you don't stick to "Champagne" (tm) - then you can try so-called "Soviet Champagne", sold as "sparkling wine" in the West. Best stuff made in ex-USSR is made in Abrau-Durso (Russia, Caucasus coast) and Noviy Svet (Ukraine, Crimea).
Many local wine "factories" in the South make great Champaign, but they are not exported and impossible to buy even in Moscow.
Abrau-Durso and Noviy Svet make a variety of sparkling wines, (champaigns), from extra-dry to sweet. A bottle of semi-dry costs about 150 rubles here in Moscow, 1 Euro = ~35 rubles.