This study presents a unified diagnostic framework for atmospheric-pressure non-equilibrium argon plasmas, addressing inconsistencies between parameters derived separately from continuum and line spectra. Using a weighted multi-objective optimization with a two-temperature generalized electron energy distribution function (GEEDF), the method simultaneously fits bremsstrahlung continuum and argon line spectra. The optimal weight parameter w is systematically determined via statistical criteria (MSLE, bias, max error) and Pareto analysis (L-curve) to balance spectral contributions. Applied to a closed-channel dielectric barrier discharge (DBD) and a plasma jet (APPJ), the method yielded a consistent bulk electron temperature of Te ~=0.6 eV, correcting the overestimation typical of conventional line-ratio methods, and an electron density of ne =1012-1013 cm-3. This approach effectively constrains the EEDF shape, providing robust diagnostics for non-equilibrium plasma kinetics.