A Pb-free FASnI3 perovskite solar cell improved by using Cu2O/ZnO as two-dimensional-based hole/electron transport nanolayers has been proposed and studied by using a SCAPS-1D solar simulator. To calibrate our study, at first, an FTO/ZnO/MAPbI3/Cu2O/Au multilayer device was simulated, and the numerical results (including a conversion efficiency of 6.06%, an open circuit potential of 0.76 V, a fill factor parameter of 64.91%, and a short circuit electric current density of 12.26 mA/cm2) were compared with the experimental results in the literature. Then, the conversion efficiency of the proposed FASnI3-based solar cell was found to improve to 7.83%. The depth profile energy levels, charge carrier concentrations, recombination rate of electron/hole pair, and the FASnI3 thickness-dependent solar cell efficiency were studied and compared with the results obtained for the MAPbI3-containing device (as a benchmark). Interestingly, the FASnI3 material required to obtain an optimized solar cell is one-half of the material required for an optimized MAPbI3-based device, with a thickness of 200 nm. These results indicate that developing more environmentally friendly perovskite solar cells is possible if suitable electron/hole transport layers are selected along with the upcoming Pb-free perovskite absorber layers.