Yes, Kurt Weill composed the beautiful music, but the French lyrics are NOT by Bertolt Brecht. Weill had fled Germany by the time he wrote this song (1934) and was working in France. The lyrics are by Roger Fernay. Weill subsequently had to escape France as well when the Nazis invaded, and he then had a nice career in America!
It seems that there is an error : the music is from Kurt Weill but the lyrics are from Roger Fernay, not from Bertold Brecht (confusion with the Dreigroshenoper, probably). However, her voice is splendid, on a par with my favorite interpretation of Teresa Stratas