The fundamental phenomenon underpinning the photonic crystal fiber’s (PCF) functionality is its capacity to trap light, enabling a broader range of applications. The study involves depositing plasmonic materials on a dual-sided open–channels based PCF–surface plasmonic resonance (SPR) sensor to detect changes in the analyte’s refractive index (RI). Through numerical investigations, the research compares the optical characteristics employing two plasmonic materials, silver (Ag) and copper (Cu). The study results show that silver exhibits a high sensitivity to wavelengths, with a maximum wavelength sensitivity of 7000 nm/RIU. Additionally, silver demonstrates a significant amplitude sensitivity of 652.98 RIU −1 . Moreover, the resolution of silver is found to be 1.43 × 10 −6 RIU within the analyte RI of 1.39. Conversely, copper exhibits a maximum wavelength sensitivity of 6000 nm/RIU, a resolution of 1.67 × 10 −6 RIU, and an amplitude sensitivity of 356.42 RIU −1 at the same RI. Additionally, the study uses Machine Learning (ML) methods, especially specific Artificial Neural Networks (ANN), to calculate optical properties, focusing on confinement loss. The plasmonic biosensor offers a simple design, suitable sensitivity, and economic feasibility, making it a viable choice for detecting biological and biochemical analytes.