Currently, the development of novel materials with high-efficiency gas adsorption properties is crucial for gas detection, environmental monitoring, and energy storage. To investigate the adsorption performance of intrinsic InN and Cu-doped InN toward three gas molecules—C₂H₂, CO, and H₂—first-principles calculations were employed to analyze their molecular structures and electronic characteristics. The results indicate that the optimal doping site occurs when Cu is adsorbed directly above the topmost In atom. Calculations of adsorption energies reveal that Cu doping reduces the adsorption energies for all three gases compared to the undoped monolayer InN. Among these, Cu–InN–CO exhibits the highest adsorption energy at –0.843 eV. The adsorption energy for Cu–InN–H2 approaches zero, indicating a weak interaction between H₂ and Cu–InN. The Cu–InN system generally gains more electrons upon gas adsorption, particularly in Cu–InN–C₂H₂, where Cu atom incorporation facilitates electron transfer from gas molecules to the material, significantly widening its bandgap. At the preset temperatures of 300, 400, and 500 K, the required dissociation time for H₂ on the Cu-InN surface exceeds 10–12 s. Cu doping enhances the intrinsic sensing capability of In, demonstrating potential for development as a novel gas sensor.