The coronavirus (COVID-19) pandemic has put the entire world at risk and caused an economic downturn in most countries. This work provided theoretical insight into a novel fiber optic-based plasmonic biosensor that can be used for sensitive detection of SARS-CoV-2. The aim was always to achieve reliable, sensitive, and reproducible detection. The proposed configuration is based on Ag-Au alloy nanoparticle films covered with a layer of graphene which promotes the molecular adsorption and a thiol-tethered DNA layer as a ligand. Here, the combination of two recent approaches in a single configuration is very promising and can only lead to considerable improvement. We have theoretically analyzed the sensor performance in terms of sensitivity and resolution. To highlight the importance of the new configuration, a comparison was made with two other sensors. One is based on gold nanoparticles incorporated into a host medium; the other is composed of a bimetallic Ag-Au layer in the massive state. The numerical results obtained have been validated and show that the proposed configuration offers better sensitivity (7100 nm\RIU) and good resolution (figure of merit; FOM = 38.88 and signal-to-noise ratio; SNR = 0.388). In addition, a parametric study was performed such as the graphene layers' number and the size of the nanoparticles.