[1] His father, Ernest Zyromski, was a literary critic and a professor at the University of Toulouse, where Jean studied law later in his life.

Coming back to civilian life in 1919, he started his career in the Administration of Social Affairs, where he eventually became an inspector.

Among members of this tendency were Léo Lagrange, Louis Lévy, Georges Dumoulin, Maurice Delépine, Ludovic Zoretti, Paul Colliette, Émile Farinet and Marceau Pivert.

Zyromski's motion, presented in the 1927 Congress of Lyon, gained 23% of the mandate; as a result, the Bataille Socialiste obtained the support of the national leadership which would refuse in 1928 and 1932 to join the Radicals in a coalition.

While acknowledging the flaw of the Soviet economic planning, he and his tendency would refuse to condemn it outright like the rest of the party, instead considering it as an experiment to take into account.

However, unlike other tendencies, such as the Neosocialists, the Plan was not seen by Zyromski's Bataille Socialiste clique as an alternative to Marxism but as something that already existed within the Marxist tradition.

[4] Zyromski played an important role in the formation of the Popular Front, being one of the main writers of the Common Action Platform signed with the Communist Party in 1935.

[2] During his time in the SFIO, Zyromski was skeptical of decolonial efforts and independence movements, drawing on the international situation created by the treaties that ended the First World War.

[9] His main motivation being anti-fascism, Zyromski condemned Léon Blum, who had become President of the Council under the Popular Front, over his non intervention policy in the Spanish Civil War.

[10] Profoundly affected by the failure of his policies during the Popular Front, the SFIO ultimately supporting the Radical Party's Édouard Daladier as President of the Council, and the French military defeat in June 1940, Zyromski retired a few weeks after the defeat in the Lot-et-Garonne department, disappearing from political and public life during the rest of the German occupation.

Within the PCF, Zyromski showed a surprisingly tolerated independence even when, in 1959, he signed a tribune in which he criticized the lack of internal democracy within the party.