Designing Photonic Crystal Fibers incorporating the Surface Plasmon Resonance Phenomenon (PCF-SPR) has led to numerous interesting applications. This investigation presents an exceptionally responsive surface plasmon resonance sensor, seamlessly integrated into a dual-core photonic crystal fiber, specifically designed for low refractive index (RI) detection. The integration of a plasmonic material, namely silver (Ag), externally deposited on the fiber structure, facilitates real-time monitoring of variations in the refractive index of the surrounding medium. To ensure long-term functionality and prevent oxidation, a thin layer of titanium dioxide (TiO2) covers the silver coating. To optimize the sensor, five key design parameters, including pitch, air hole diameter, and silver thickness, are fine-tuned using the Taguchi L8(25) orthogonal array. The optimal results obtained present spectral and amplitude sensitivities that reach remarkable values of 10,000 nm/RIU and 235,882 RIU-1, respectively. In addition, Artificial Neural Network (ANN) optimization techniques, specifically Multi-Layer Perceptron (MLP) and Particle Swarm Optimization (PSO), are used to predict a critical optical property of the sensor confinement loss (αloss). These predictions are derived from the same input structure parameters that are present in the full L32(25) design experiment. A genetic algorithm (GA) is then applied for optimization with the goal of maximizing the confinement loss. Our results highlight the effectiveness of training PSO artificial neural networks and demonstrate their ability to quickly and accurately predict results for unknown geometric dimensions, demonstrating their significant potential in this innovative context. The proposed sensor design can be used for various applications including pharmaceutical inspection and detection of low refractive index analytes.