In this study, we investigated numerically the plasmon response of a planar negative-index metamaterial composed of symmetric molecular orientations of Au ring/disk nanocavities in a heptamer cluster. Using the plasmon hybridization theory and considering the optical response of an individual nanocluster, we determined the accurate geometrical sizes for a ring/disk nanocavity heptamer. It is shown that the proposed well-organized nanocluster can be tailored to support strong and sharp Fano resonances in the visible spectrum. Surrounding and filling the heptamer clusters by various metasurfaces with different chemical characteristics, and illuminating the structure with an incident light source, we proved that this configuration reflects low losses and isotropic features, including a pronounced Fano dip in the visible spectrum. Technically, employing numerical methods and tuning the geometrical sizes of the structure, we tuned and induced the Fano dip in the visible range, while the dark and bright plasmon resonance extremes are blueshifted to shorter wavelengths dramatically. Considering the calculated transmission window, we quantified the effective refractive index for the structure, while the substance of the substrate material was varied. Using Si, GaP, and InP semiconductors as substrate materials, we calculated and compared the corresponding figure of merit (FOM) for different regimes. The highest possible FOM was obtained for the GaP-Au-GaP negative-refractive-index metamaterial composed of ring/disk nanocavity heptamers as 62.4 at λ∼690 nm (arounnd the position of the Fano dip). Despite the outstanding symmetric nature of the suggested heptamer array, we provided sharp Fano dips by the appropriate tuning of the geometrical and chemical parameters. This study yields a method to employ ring/disk nanocavity heptamers as a negative-refractive-index metamaterial in designing highly accurate localization of surface plasmon resonance sensing devices and biochemical sensors.