Two-dimensional (2D) heterostructure materials show captivating properties for application in surface plasmon resonance (SPR) sensors. A fluoride fiber-based SPR sensor is proposed and simulated with the inclusion of a 2D heterostructure as the analyte interacting layer. The monolayers of two 2D heterostructures (BlueP/MoS2 and BlueP/WS2, respectively) are considered in near infrared (NIR). In NIR, an HBL (62HfF4-33BaF2-5LaF3) fluoride glass core and NaF clad are considered. The emphasis is placed on figure of merit (FOM) enhancement via optimization of radiation damping through simultaneous tuning of Ag thickness (dm) and NIR wavelength (λ) at the Ag-2D heterostructure–analyte interfaces. Field distribution analysis is performed in order to understand the interaction of NIR signal with analyte at optimum radiation damping (ORD) condition. While the ORD leads to significantly larger FOM for both, the BlueP/MoS2 (FOM = 19179.69 RIU−1 (RIU: refractive index unit) at dm = 38.2 nm and λ = 813.4 nm)-based sensor shows massively larger FOM compared with the BlueP/WS2 (FOM = 7371.30 RIU−1 at dm = 38.2 nm and λ = 811.2 nm)-based sensor. The overall sensing performance was more methodically evaluated in terms of the low degree of photodamage of the analyte, low signal scattering, high power loss, and large field variation. The BlueP/MoS2-based fiber SPR sensor under ORD conditions opens up new paths for biosensing with highly enhanced overall performance.