A metallic fishnet metamaterial structure in sub-THz region is presented. The proposed structure is based on hexagonal resonators. Simulations have been performed by a 3D full-wave electromagnetic simulator and a negative refractive index has been observed at the frequency range between 0.55 and 0.70 THz with the help of the graphene layer. In order to observe the effect of the graphene layer, the metamaterial structure has been simulated and examined before and after graphene integration. Significant modification in the propagation properties has been observed after the graphene integration. Change in S-parameters with the size variation of hexagonal resonators and alteration in graphene thickness are also presented as a parametric study to show the tunability of the structure. Suitability of the metamaterial for sensor applications has been investigated. The proposed metamaterial structure is promising to be effectively used for tunability and sensor applications.