The robust bonding between Fe and N atoms has the potential to fabricate a ferromagnetic Fe2N monolayer of a square lattice independently of the symmetry of the substrate. The electronic and magnetic properties tuned by the symmetry of the substrates are investigated by comparing the results of scanning tunnel microscopy and x-ray absorption spectroscopy/magnetic circular dichroism of the square Fe2N monolayer on the Cu(1 1 1) substrate with that on the Cu(0 0 1) substrate. A periodic electronic modulation of the Fe2N monolayer on the Cu(1 1 1) substrate is induced by the stripe superlattice due to the difference of the lattice symmetry between the Fe2N monolayer and the Cu(1 1 1) substrate. The electronic and magnetic properties of the monolayer are largely affected by the hybridization with the Cu substrate and the Fe magnetic moment is much reduced compared to the monolayer on the Cu(0 0 1) substrate.