Fairly sure Tim Mcllrath confirmed it’s a Russian version of L’Internationale in an interview. Genius dot com got it wrong on their lyrics page.

Songfacts: Nowhere Generation opens with a brief audio clip of a song called “The Internationale” (aka “L’Internationale”).

McIlrath: “L’Internationale” has sort of become an anthem for the left-wing movements throughout history. Different cultures have kept the rhythm and the song the same, but they changed the lyrics to suit whatever struggle they were going through.

McIlrath: I think it’s like the music to the French national anthem, but we use a Russian version to kick the record off. It’s just a nod to a lot of the labor movements around the world, and also to point out a lot of the struggles that we deal with today are something that we’ve dealt with historically.

https://www.songfacts.com/blog/interviews/tim-mcilrath-rise-against