To contribute to the optimisation of the performances of the nano-devices (storage medium, bio sensors…), we have theoretically studied the structural, magnetic and magneto-optical properties of the Fe ultrathin films grown by epitaxy on semi-infinite Cu(001) substrate using a relativistic approach into the DFT framework. Structurally, we found that the body centered tetragon Fe can be stabilized onto the Cu(001) oriented substrate with a tetragonality ratio larger than the unity. The magnetic behaviour is characterized by an enhanced magnetic moment with respect to the bulk one with a ferromagnetic intra and inter-atomic plane coupling. The polar magneto-optical Kerr effect spectra are characterized by a negative peak in the visible range mainly coming from the d → p interband transitions.