After joining the French Section of the Workers' International in 1934, he worked as a writer for the newspaper Le Populaire.
Tasca joined the exiled Italian Socialist Party (PSI) and supported the POUM during the Spanish Civil War.
After the signing of the Molotov–Ribbentrop Pact in August 1939 and the consequent resignation of Pietro Nenni, he became one of three joint leaders of the PSI.
He was arrested in September 1944 after the Liberation of France and was charged with collaborationism but was released only a month later after it emerged that he had secretly worked with a Belgian anti-fascist network since 1941.
His daughter, Catherine Tasca, was France's Minister of Culture from 2000 to 2002 and a senator from 2004 to 2017 for the French Socialist Party.