We present a dual-mode optical sensing strategy for selective and sensitive detection of sulfide ions (S²⁻), employing copper-anchored nitrogen-doped graphene quantum dots (Cu@N-GQDs) as bifunctional nanozymes. The Cu@N-GQDs were synthesized via citric acid pyrolysis in the presence of ammonium hydroxide (serving as both nitrogen source and reductant) and copper chloride, leading to uniform incorporation of copper oxide species onto the N-GQD surface. The resulting nanohybrids exhibit two synergistic functionalities: intrinsic fluorescence comparable to pristine N-GQDs, and significantly enhanced peroxidase-like catalytic activity attributed to the anchored copper species. Upon interaction with sulfide ions, the system undergoes a dual-optical response: (i) fluorescence quenching via Cu-S complexation, and (ii) inhibition of peroxidase-like activity due to the deactivation of Cu catalytic centers via the interaction with S²⁻. This dual-signal strategy enables sensitive quantification of S²⁻, achieving detection limits of 0.5 µM (fluorescence) and 3.5 µM (colorimetry). The sensor demonstrates excellent selectivity over competing substances and high reliability and precision in real tap water samples. These findings highlight the potential of Cu@N-GQDs as robust, bifunctional, and field-deployable nanozyme probes for environmental and biomedical sulfide ion monitoring.