This study presents a hybrid deep learning (DL) approach for designing and optimizing a photonic crystal fiber (PCF)-based surface plasmon resonance (SPR) multi-analyte biosensor. Using a simulation based on the finite element method (FEM), we generated a comprehensive data set that captures various sensor parameters and refractive index (RI) values. A hybrid recurrent neural network long-short-term memory (RNN-LSTM) model was developed to predict confinement loss (CL), which showed superior performance with an MSE of 0.0014, an MAE of 0.0188, and an R2 of 0.9510 compared to other DL and machine learning (ML) models. The proposed model shows a maximum amplitude sensitivity (AS) of 3102.41 RIU−1, a wavelength sensitivity (WS) of 10,000 nm/RIU, and a sensor resolution (SR) of 1 × 10−5. The effectiveness of the model was validated through extensive analysis, including ablation studies and SHAP-based explainability analysis. Our findings highlight the potential of DL to improve multi-analyte biosensor design and performance prediction.