Kastler was born in Guebwiller (Alsace, German Empire) and later attended the Lycée Bartholdi in Colmar, Alsace, and École Normale Supérieure in Paris in 1921. After his studies, in 1926 he began teaching physics at the Lycée of Mulhouse, and then taught at the University of Bordeaux, where he was a university professor until 1941. Georges Bruhat asked him to come back to the École Normale Supérieure, where he finally obtained a chair in 1952.
Kastler also wrote poetry (in German). In 1971 he published Europe, ma patrie: Deutsche Lieder eines französischen Europäers (i.e. Europe, my fatherland: German songs of a French European).
Professor Kastler spent most of his research career at the Ecole Normale Supérieure in Paris where he started after the war with his student, Jean Brossel a small research group on spectroscopy.