Châtelet was a student at the École normale supérieure (Paris) from 1905 to 1908, succeeding to the Agrégation (a highly selective competitive examination for future high-school teachers) in 1908.

After his retirement as dean in 1954, Châtelet began participating in political movements at the forefront of the downfall of the French Fourth Republic by joining the Rationalist Union in 1955.

In 1958 Albert Châtelet was chosen to represent the Union of Democratic Forces as its candidate during the French presidential election.

He introduced the research of Kurt Hensel, Helmut Hasse, and the German school of p-adic number theorists into France.

In 1920 he gave a plenary address at the International Congress of Mathematicians in Strasbourg: Loi de Réciprocité Abélienne.