In the present work, the sensing performance analysis of a surface plasmon resonance (SPR) sensor for biological and chemical applications is reported. The structure studied consists of a silver nanofilm, the hybrid nanostructure of bismuth ferrite material (BiFeO3), and a nickel nanofilm covered by a layer of perovskite CH3NH3PbBr3 (MAPbBr3) nanomaterial. Our analyses are based on the finite element method (FEM) and a monochromatic excitation of wavelength 633 nm. We numerically analyzed performance parameters such as angular sensitivity, sensitivity enhancement, factor of merit (FoM) and electric field distribution. We have shown that the proposed SPR biosensor exhibits very good detection performance in terms of sensitivity and FoM. Compared with the conventional SPR structure, the 2D nanomaterials have excellent properties, such as stronger absorption capacity, which improves the biological and chemical sensing ability of the sensor. The sensitivity and FoM of the optimized biosensor reaches 408 deg/RIU with 240% enhancement, and 93.12 RIU−1 with 138.78% improvement respectively, when the perovskite material layer covered the BK7/Ag/BiFeO3/Ni hybrid nanostructure; for a 0.005 RIU variation in the refractive index of the sensing medium. Therefore, our proposed design and study would be practically suitable for bio/chemical sensing and in biomedical application has excellent performance, with the available fabrication technologies.