Surface plasmon resonance (SPR)-based sensors have attracted significant attention as highly sensitive platforms for the non-invasive detection of glucose. In this study, an SPR biosensor with a CsF/Cu/FASnI₃/Black Phosphorus (BP)/Graphene multilayer structure was designed for glucose detection in urine samples and analyzed using the Transfer Matrix Method (TMM). To achieve optimal performance, the thickness of the copper layer as well as the number of black phosphorus and graphene layers were systematically optimized. The results demonstrated that the optimized configuration, consisting of a 50 nm copper layer, three layers of black phosphorus, and a single graphene layer, exhibited the best sensing performance, achieving a maximum sensitivity of 348 deg/RIU and a figure of merit (FOM) of 91 RIU⁻¹. Although the incorporation of graphene resulted in a slight reduction in sensitivity, it significantly improved the chemical stability of the sensor by protecting black phosphorus against oxidation, thereby enhancing its practical applicability. Furthermore, comparison with previously reported SPR biosensors revealed that the proposed design, which integrates a copper plasmonic layer with a perovskite layer, black phosphorus, and graphene, provides an excellent balance between sensitivity, chemical stability, and fabrication cost. These findings highlight the proposed sensor as a promising candidate for the development of low-cost, high-performance SPR biosensors for non-invasive glucose monitoring