Born in Prague, Bohemia (then part of Austria-Hungary), Rambousek embarked on a versatile sporting career. He first gained prominence as a footballer, playing as a forward for Sparta Prague, one of Czechoslovakia's leading clubs, during the 1910s and 1920s. He was a member of the celebrated "Iron Sparta" team, which achieved considerable domestic success.
However, it was in ice hockey that Rambousek's impact was most profound. He played as a forward for LTC Prague, a club that dominated European ice hockey during the interwar period. With LTC, he secured numerous national championships and prestigious international tournament victories. Rambousek also proudly represented the Czechoslovak national ice hockey team, participating in multiple World Championships and Olympic Games. He was part of the national squad that earned a silver medal at the 1922 European Championship.
Following his illustrious playing career, Rambousek transitioned into coaching and management. He coached both ice hockey and football teams, including a tenure with LTC Prague and the Czechoslovak national ice hockey team. His strategic insights and dedication were instrumental in fostering ice hockey talent and advancing the sport during what is considered a golden era for Czechoslovak hockey. Beyond coaching, Rambousek held various administrative roles within Czechoslovak sports federations, contributing significantly to the organizational structure and development of sports at a national level.
František Rambousek is remembered as a pioneering figure who excelled as both a player and a leader. His multifaceted contributions left an indelible mark on Czech sports history, particularly during the interwar period, and he remains a revered name in the annals of Czechoslovak sports. He passed away in Prague at the age of 54.