Manuel Neuer made 10 saves to deny RB Salzburg, registering another strong performance.
Bayern Munich winger Kingsley Coman picked up where he left off last season with two goals in a 4-0 home rout of Atletico Madrid on Wednesday
Against first-time finalists PSG, Bayern were worthy winners of their sixth European Cup, their third in the Champions League era.
Kingsley Coman scored the only goal of the Champions League final to wrap up the treble for Bayern Munich, who had already won the Bundesliga and German Cup.
France cruised past Albania 4-1 on Saturday to move back to the top of their group in qualifying for Euro 2020.