The structural, electronic, magnetic, optical, and thermoelectric properties of diluted magnetic semiconductors (DMS) based on the chalcogenide compounds Au3CoS2, Au2Co2S2, and AuCo3S2 have been investigated using all-electron first-principles calculations. We have used the GGA-PBEsol and the around mean-field (AMF) correction scheme (GGA-PBEsol + U) for the exchange-correlation energies. Firstly, we calculated the equilibrium ground state of properties. Afterward, we evaluated the magneto-electronic properties using the GGA-PBEsol and GGA-PBEsol + U approaches. The computed spin-polarized band structures and density of states revealed the half-metallic ferromagnetic behavior for the studied compounds from both approaches. The half-metallicity is mainly due to the p-d hybridization of S and Co atoms. We also estimated the Curie temperatures using the mean-field approximation, and the results exceeded the ambient temperature. The real and imaginary components of the dielectric function, as well as the refractive index and reflectivity, were calculated up to 13.0 eV for both spin directions to explore the optical responses of AuCo3S2, Au2Co2S2, and Au3CoS2 compounds. The thermoelectric responses have also been reported for the spin-up orientation using the semi-classical Boltzmann transport theory and indicate that the half-metallic behavior is maintained at high temperatures. Finally, both the importance and potential applications of the studied compounds are discussed in this study.