Let me be ahistorical in a way that completely makes sense.
To me, this is what Saint-Just's epic line means:
(Translation of the lyrics for the second video.)
To me, this is what he means with "this independent life" he's given to himself "in the centuries and in the skies". That's his legacy. That's his spirit. He doesn't know it, it's just a small flicker of hope, but he's throwing his soul to the future -- "L'homme obligé de s'isoler du monde et de lui-même jette son ancre dans l'avenir, et presse sur son cœur la postérité innocente des maux présents." ("The man who must isolate himself from the world and from himself casts his anchor into the future, and presses to his heart the posterity innocent of present evils.")
--he doesn't know, but that's how he'll live independently forever in the centuries and in the skies. His voice will always echo in the rage of the youth that screams against injustice and absurdity.
