In the 1960s, Demazure was a student of Alexandre Grothendieck, and, together with Grothendieck, he ran and edited the Séminaire de Géométrie Algébrique du Bois Marie on group schemes at the Institut des Hautes Études Scientifiques near Paris from 1962 to 1964.

Demazure obtained his doctorate from the Université de Paris in 1965 under Grothendieck's supervision, with a dissertation entitled Schémas en groupes réductifs.

[9] A 1970 paper of Demazure on subgroups of the Cremona group[10] has been later recognized as the beginning of the study of toric varieties.

Demazure's work in this area was marred by a dependence on a false lemma in an earlier paper (also by Demazure); the flaw was pointed out by Victor Kac, and subsequent research clarified the conditions under which the formula remains valid.

Austrian mathematician Erwin Kruppa had many years earlier narrowed the number of possible scenes to eleven, and Demazure provided the first complete solution to the problem.