From 1957 to 1959, he prepared for archery at the École spéciale militaire de Saint-Cyr at the Prytanée National Militaire, and became eligible, but changed his mind. He joined Socialisme ou Barbarie, without playing a "remarkable role" according to the account of Cornelius Castoriadis. He fought in the Algerian War. In 1965, with the help of Jacques Baynac, he opened La Vieille Taupe bookstore, which was linked to the group Pouvoir ouvrier, a French ultra-left group sharing a critical stance to Marxism as Socialisme ou Barbarie from whom they had split in 1963.
In September 1967, when his exclusion was imminent, Guillaume and Beynac left Pouvoir ouvrier, followed by most of the young members of the group. Then, La Vieille Taupe became the name of a small, informal group of people interested in studying the ultra left, the Situationist International, and Rosa Luxemburg. The current bookstore named La Vieille Taupe in Paris sells books that are fundamental to these movements.
The politics of Guillaume and other ultra-left Holocaust deniers (including Serge Thion and Paul Rassinier) have been characterized as "anarcho-Marxist." According to Alain Finkielkraut, Guillaume's commitment to Holocaust denial stemmed from his ultra-left politics, rather than from antisemitism. The genocide of the Jews was seen by Guillaume and others as a distraction from class struggle, and as playing into the hands of Zionist and Stalinist ideologies, and was hence denied.[7][8]
