Puč's international career lasted from 1926 to 1939; in that time, he played 61 matches for Czechoslovakia, scoring 35 goals. He played for Czechoslovakia in the 1934 FIFA World Cup scoring two goals, including one in the final, a 2–1 loss against Italy, and also played in the 1938 edition. Puč spent most of his club career with Slavia Prague.