Two-layer foils of nanotwinned copper with graphene nanoinclusions were fabricated by electrochemical deposition from 1M CuSO4*6H2O aqueous solution containing graphene-graphite mixture stabilized by non-ionic surfactants (Pluronic F-127 and Polyacrilic acid - PAC). The microstructure of the outer foils surface was examined by Scanning Electron Microscopy, the microstructure of the inner foils surface was characterized by Atomic Force Microscopy. XRD analysis proved that the deposition of the thin copper layer on the wafer in case of suspension stabilized by Pluronic F-127 surfactant results in the nanotwinned copper growth. Raman Spectroscopy showed that the use of stabilized suspensions provides the graphene insertion into the foils in a form of nanoinclusions i.e. flakes with 4-6 graphene layers. The amount of graphene in the foils depends on the composition of the graphenegraphite suspension and on the surfactant type. Nanoindentation tests were carried out for both inner and outer surfaces of the foils. The microhardness of inner surface of the foils fabricated using the suspension stabilized by Pluronic F-127 surfactant lies in the range of 2 to 3 GPa, while the elastic modulus exceeds 100 GPa.