Pleyer was born in Vienna, the capital city of Austria. He played for Brigittenauer AC in his home country before moving to France in 1933 to play for Stade Rennais UC. Pleyer spent the rest of his career playing for Rennes appearing in over 200 matches for the club. In 1935, he played on the team that reached the final of the Coupe de France. In the final, Rennes were defeated 3–0 by Marseille. In December 1936, Player acquired French citizenship and adopted the name François, the French anglicisation of Franz.
In 1939, Pleyer's football career was put on hold due to World War II. He served for France during the war and, following its conclusion, returned to Rennes. Pleyer spent his latter years with the club serving in a player-coach role. His final appearance with Rennes was in May 1951 at the age of 40.