Achour is the daughter of the Tunisian film director and actor Lotfi Achour and a Russian mother who is a playwright. Her older brother is a playwright, and she has a younger brother. Achour grew up in the 12th arrondissement of Paris in an atmosphere that was "an artistic milieu, but not bourgeois."[1] As a child, she accompanied her parents during their rehearsals and at their performances.[2]