High-quality films of the ferromagnetic semiconductor EuO are grown on epitaxial graphene on Ir(111) and investigated in situ with scanning tunneling microscopy and spectroscopy. Electron scattering at defects leads to standing-wave patterns, manifesting the existence of a surface state in EuO. The surface state is analyzed at different temperatures and energies. We observe a pronounced energy shift of the surface state when cooling down below the Curie temperature TC, which indicates a spin polarization of this state at low temperatures. The experimental results are in agreement with corresponding density functional theory calculations.