A plasmonic material-coated circular-shaped photonic crystal fiber (C-PCF) sensor based on surface plasmon resonance (SPR) is proposed to explore the optical guiding performance of the refractive index (RI) sensing at 1.7–3.7 μm. A twin resonance coupling profile is observed by selectively infiltrating liquid using finite element method (FEM). A nano-ring gold layer with a magnesium fluoride (MgF${}_2$) coating and fused silica are used as plasmonic and base material, respectively, that help to achieve maximum sensing performance. RI analytes are highly sensitive to SPR and are injected into the outmost air holes of the cladding. The highest sensitivity of 27,958.49 nm/RIU, birefringence of 3.9 × ${10}^{-4}$, resolution of 3.70094 × ${10}^{-5}$ RIU, and transmittance dip of −34 dB are achieved. The proposed work is a purely numerical simulation with proper optimization. The value of optimization has been referred to with an experimental tolerance value, but at the same time it has been ensured that it is not fabricated and tested. In summary, the explored C-PCF can widely be eligible for RI-based sensing applications for its excellent performance, which makes it a solid candidate for next generation biosensing applications.