We consider the process of four-wave mixing in an array of gold nanowires strongly coupled to a gold film. Using full-wave simulations, we perform a quantitative comparison of the four-wave mixing efficiency associated with a bare film and films with nanowire arrays. We find that the strongly localized surface plasmon resonances of the coupled nanowires provide an additional local field enhancement that, along with the delocalized surface plasmon of the film, produces an overall four-wave mixing efficiency enhancement of up to six orders of magnitude over that of the bare film. The enhancement occurs over a wide range of excitation angles. The film-coupled nanowire array is easily amenable to nanofabrication, and could find application as an ultra-compact component for integrated photonic and quantum optic systems.