He was a French Resistance fighter (under the aliases "Saint-Just", "Berneix" or "Rossini"), deputy in the National Assembly, a senator, an important leader of the Gaullist movement, and secretary of state and mayor of Rueil-Malmaison.

In 1943, he was secretary general of the Mouvements Unis de la Résistance (United movements of the Resistance) (MUR).

He participated in the development of Rassemblement du peuple français (Rally of the French People) (RPF) from its founding in 1947.

He became the general secretary of the Gaullist movement on 7 December 1962 after the success of the UNR in November, a position he held until 19 January 1968, when he was replaced by Robert Poujade.

Baumel appeared as a witness in Patrick Pesnot's 2005 television documentary, La traversée du désert (Crossing the Desert).