Photoemission, from core levels and valence band, and low-energy electron diffraction (LEED) have been employed to investigate the electronic and structural properties of graphene-ferromagnetic (G-FM) systems, obtained by intercalation of one monolayer (1 ML) and several layers (4 ML) of Co on G grown on Ir(111). Upon intercalation of 1 ML of Co, the Co lattice is resized to match the Ir-Ir lattice parameter, resulting in a mismatched G/Co/Ir(111) system. The intercalation of further Co layers leads to a relaxation of the Co lattice and a progressive formation of a commensurate G layer lying on top. We show the C $1s$ line shape and the band structure of G in the two artificial phases, mismatched and commensurate G/Co, through a comparison with the electronic structure of G grown directly on a Co thick film. Our results show that while the G valence band mainly reflects the hybridization with the $d$ states of Co, regardless of the structural phase, the C $1s$ line shape is very sensitive to the rumpling of the G layer and the coordination of carbon atoms with the underlying Co. Even in the commensurate ($1\ifmmode\times\else×\fi{}1$) G/Co phase, where graphene is in register with the Co film, from the angular dependence of the C $1s$ core level we infer the presence of more than a single component, due to inequivalent adsorption sites of carbon sublattices.