A simple theoretical model was developed to analyze the extinction spectrum of gold nanoparticles (AuNPs) on the fiber core and glass surfaces in order to aid the determination of the surface coverage and surface distribution of the AuNPs on the fiber core surface for sensitivity optimization of the fiber optic particle plasmon resonance (FOPPR) sensor. The extinction spectrum of AuNPs comprises of the interband absorption of AuNPs, non-interacting plasmon resonance (PR) band due to isolated AuNPs, and coupled PR band of interacting AuNPs. When the surface coverage is smaller than 12.2%, the plasmon coupling effect can almost be ignored. This method is also applied to understand the refractive index sensitivity of the FOPPR sensor with respect to the non-interacting PR band and the coupled PR band. In terms of wavelength sensitivity at a surface coverage of 18.6%, the refractive index sensitivity of the coupled PR band (205.5 nm/RIU) is greater than that of the non-interacting PR band (349.1 nm/RIU). In terms of extinction sensitivity, refractive index sensitivity of the coupled PR band (−3.86/RIU) is similar to that of the non-interacting PR band (−3.93/RIU). Both maximum wavelength and extinction sensitivities were found at a surface coverage of 15.2%.