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.
After the split of the country into the Czech Republic and Slovakia and the corresponding national teams, Jan Koller surpassed Puč's record in 2005. Puč died in 1988 aged 80.