Résumé
Let$(g,\delta_\hbar)$be a Lie bialgebra. Let$(U_\hbar(g),\Delta_\hbar)$a quantization of$(g,\delta_\hbar)$through Etingof-Kazhdan functor. We prove the existence of a$L_\infty$ -morphism between the Lie algebra$C(\g)=\Lambda(g)$and the tensor algebra$TU=T(U_\hbar(g)[-1])$with Lie algebra structure given by the Gerstenhaber bracket. When$(g,\delta_\hbar,r)$is a coboundary Lie bialgebra, we deduce from the formality morphism the existence of a quantization$R$of$r$ .