In this paper, a new label-free DNA nanosensor based on a top-gated (TG) metal–ferroelectric–metal (MFM) graphene nanoribbon field-effect transistor (TG-MFM GNRFET) is proposed through a simulation approach. The DNA sensing principle is founded on the dielectric modulation concept. The computational method employed to evaluate the proposed nanobiosensor relies on the coupled solutions of a rigorous quantum simulation with the Landau–Khalatnikov equation, considering ballistic transport conditions. The investigation analyzes the effects of DNA molecules on nanodevice behavior, encompassing potential distribution, ferroelectric-induced gate voltage amplification, transfer characteristics, subthreshold swing, and current ratio. It has been observed that the feature of ferroelectric-induced gate voltage amplification using the integrated MFM structure can significantly enhance the biosensor’s sensitivity to DNA molecules, whether in terms of threshold voltage shift or drain current variation. Additionally, we propose the current ratio as a sensing metric due to its ability to consider all DNA-induced modulations of electrical parameters, specifically the increase in on-state current and the decrease in off-state current and subthreshold swing. The obtained results indicate that the proposed negative-capacitance GNRFET-based DNA nanosensor could be considered an intriguing option for advanced point-of-care testing.