In recent years, the plasma gap resonance maintained by metal-film-coupled nanostructures has attracted extensive attention. This mainly originates from its flexible control of the spectral response and significantly enhanced field strength at the nanoparticle–film junction. In the present study, the tunability of local surface plasmon resonances (LSPRs) of nanorods coupled to a gold film is studied theoretically. To this end, the plasmonic resonances in the nanostructure of individual silver nanorod–gold film (AgNR-film) with different parameters are investigated. Obtained results show that the refractive index sensitivity (S) of nanostructures to the environment increases as the aspect ratio (Ar) of nanostructures increase. It is found that when the aspect ratio (Ar) is set to 3.5, the figure of merit (FOM) is the highest. Moreover, the variation in the gap distances of the nanorod monomer–gold film, electric field distribution of nanorods dimer, and the corresponding impact on the gold film are studied. It is concluded that the gap size of nanostructures has an exponential correlation with the resonance wavelength. Considering the remarkable influence of the gap size and the surrounding medium environment on the spectral shift of AgNR-film nanostructures, potential applications of the structure as a refractive index sensor and biomolecule measurement are proposed.