Before the 1971–72 NHL season the Sabres drafted Perreault's Junior Canadiens teammate, Rick Martin, with their first pick. The two jelled as a tandem with each scoring 74 points. Late in the season the Sabres traded Eddie Shack for Rene Robert. The trio formed one of the decade's most memorable and exciting lines, known as "The French Connection" with Robert on right wing and Martin on left wing. They ended the following 1972–73 season sweeping the top three scoring positions for the team and leading the franchise to its first playoff appearance with Perreault winning the Lady Byng Trophy as the most gentlemanly player. In 1973–74, Perreault endured a broken leg that limited him to 55 games.