Magnetically doped CeO₂ is a dilute magnetic semiconductor, promising for various applications in photonics, but the origin of its ferromagnetic properties is not fully understood. Here, thin films of Ce₁₋ₓCoₓO_(2-δ) prepared by pulsed laser deposition on MgO (x=0.05 and 0.10) and oxidized Si (x=0.20) substrates were systematically studied by spectroscopic ellipsometry and magneto-optical spectroscopy. Both diagonal and off-diagonal permittivity-tensor elements were obtained. Diagonal spectra revealed two optical transitions between oxygen and cerium states. Off-diagonal spectra revealed two paramagnetic transitions involving cobalt ions, from which an essential influence of cobalt doping on resulting ferromagnetic properties of CeO₂ was inferred. The full permittivity-tensor spectra are provided for further use in prospective modelling of magneto-optical device concepts.