Quantum well states of Ag films grown on stepped Au(111) surfaces are shown to undergo lateral scattering, in analogy with surface states of vicinal Ag(111). Applying angle resolved photoemission spectroscopy we observe quantum well bands with zone-folding and gap openings driven by surface/interface step lattice scattering. Experiments performed on a curved Au(111) substrate allow us to determine a subtle terrace-size effect, i.e., a fine step-density-dependent upward shift of quantum well bands. This energy shift is explained as mainly due to the periodically stepped crystal potential offset at the interface side of the film. Finally, the surface state of the stepped Ag film is analyzed with both photoemission and scanning tunneling microscopy. We observe that the stepped film interface also affects the surface state energy, which exhibits a larger terrace-size effect compared to surface states of bulk vicinal Ag(111) crystals.