We show that the plasmon resonances of a metallic nanoparticle interacting with the surface plasmons of a metallic film is an electromagnetic analogue of the spinless Anderson-Fano model. This is the same model used to describe the interaction of a localized electronic state with a continuous band of electronic states. The three characteristic regimes of this model are realized here, where the energy of the nanoparticle plasmon resonance lies above, within, or below the energy band of surface plasmon states. These three interaction regimes are controlled by film thickness. The latter regime is experimentally observed and identified.