František Valošek was a Czechoslovak football player who spent most of his career with FC Baník Ostrava. In 1957 Valošek made his senior début with Jiskra Frýdek before joining Dukla Olomouc. By 1959 he had signed for Baník Ostrava, spending the next seven seasons with the club. An attacking forward, he played in 150 matches for the side, scoring 54 goals. Between 1961 and 1965 he made six appearances for the Czechoslovakia national football team, playing in several friendlies along with qualifying matches for the 1966 FIFA World Cup. Valošek also won a silver medal at the 1964 Tokyo Olympics where he scored the only goal in the 1–0 victory against Brazil in the group stage of the tournament. After his playing career he returned to Baník Ostrava, coaching their youth side for 15 years.