[1][2] He graduated from the École normale supérieure in 1968, and completed his doctoral thesis, Recherches sur les pastourelles médiévales, in 1970 under the direction of Pierre le Gentil [fr] while working as an assistant professor at Paris-Sorbonne University.

Working with Le Gentil, Zink completed a second thesis, La Prédication en langue romane avant 1300 in 1975, and the following year became a full professor at the University of Toulouse-Le Mirail.

[3] He was elected to the Académie des Inscriptions et Belles-Lettres in 2000, filling the vacant seat of medievalist Félix Lecoy [fr].

He was named chair of the board of directors of the École normale supérieure in 2004, resigning his seat the following year in protest of Monique Canto-Sperber becoming the head of the institution.

In 2017, Zink was elected to seat 37 of the Académie française, filling the vacancy left by the death of historian René Girard.