I will present (in French) a generalization of the Blakers-Massey theorem which applies to a family of factorization systems (satisfying some axioms) on an arbitrary infinity topos. The classical theorem is obtained by considering the category of spaces and the n-trucated/n-connected factorization system. The proof itself is inspired by previous work on proving the Blakers-Massey theorem in Homotopy Type Theory, that is, using only the internal language of a higher topos. Time permitting, I will discuss applications to Goodwillie's Calculus of Funtors.