Two-dimensional (2D) heterostructure-based fluoride fiber surface plasmon resonance (SPR) sensor designs are simulated and analyzed while emphasizing figure of merit (FOM) enhancement in the near-infrared (NIR) spectral region. Through simultaneous optimization of NIR wavelength and Ag layer thickness, exceptionally large FOM values of 15,650.75 RIU-1 and 12,409.30 RIU-1 are achieved for BlueP/MoS2-based and BlueP/WS2-based fiber SPR sensors, respectively. The results are explained in terms of tunable radiation damping, power loss, and corresponding field enhancement. These FOM values are significantly greater than recently reported sensors. The BlueP/MoS2-based sensor with 48.8 nm Ag film and at 738.4 nm wavelength provides an all-round large FOM.