Based on the unique properties of optical Fano resonance and plasmonic-waveguide coupling systems, this paper explores a novel refractive index concentration sensor structure. The sensor structure is composed of a metal–insulator–metal (MIM) waveguide and two identically shaped and sized double-tooth ring couplers (DTR). The performance structure of the nanoscale refractive index sensor with DTR cavity was comprehensively assessed using the finite element method (FEM). Due to the impact of various geometric parameters on the sensing characteristics, including the rotation angles, the widths between the double-tooth rings, and the gaps between the cavity and the waveguide, we identified an optimal novel refractive index sensor structure that boasts the best performance indices. Finally, the DTR cavity sensor achieved a sensitivity of 4137 nm/RIU and Figure of merit (FOM) of 59.1. Given the high complexity and sensitivity of the overall structure, this nanoscale refractive index sensor can be applied to the detection of oil concentration in industrial oil–water mixtures, yielding highly precise results.