We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization group and a self-consistent variational approach to obtain the critical points and phases at T=0. We predict a quantum phase transition toward a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the dc resistivity of the wire.