In this study, we used the density functional theory (DFT) method to analyze the effect of Cu insertion on the structural stability, electronic, magnetic, optical and thermoelectric properties of the hexagonal ZnS monolayer (h-ZnS-2D). Our findings show that Cu replaces zinc sites by giving a stable planar structure in Ferromagnetic (FM) phase with slight decrease in the lattice parameter. A p-type semiconductor with a direct band gap that decreases with increasing Cu concentration was obtained. The half-metallic character found for low Cu concentrations let consider the h-Zn1-xCuxS-2D for potential applications in spintronic devices. The optical properties show that the h-Zn1-xCuxS-2D monolayers have high absorption and low transmittance in the UV range. The improved figure of merit of h-Zn1-xCuxS-2D due to increased electrical conductivity and decreased thermal conductivity with Cu content, makes these nanostructures a promising absorber for thin-film solar cells and suitable for solar thermal energy conversion technologies.