Optical properties and surface structure of graphene films grown on thin 1-μm copper layer using the chemical vapor deposition method were investigated applying spectroscopic ellipsometry and nanoscopic measurements. Angle-variable ellipsometry measurements were performed to analyze features of optical conductivity and dispersion of the complex refraction index. Significant enhancement of the absorption band in the graphene single layer with respect to the bulk graphite was observed due to interaction between excited localized surface plasmon at the surface of thin Cu layer and graphene’s electrons. Scanning tunneling microscopy measurements with atomic spatial resolution revealed vertical crystal lattice structure of the deposited graphene layer. The obtained results provide direct evidence of the strong influence of the growth conditions on electronic and optical behavior of graphene films.