Mg and Cu co-doped ZnO thin films were fabricated on a FTO glass substrate by the electrochemical method at a constant current density of 3.5 mA/cm². Mg:Cu:ZnO films with a 3 wt.% Mg concentration and varying concentrations of 0, 2, 3, and 4 wt.% Cu are designated as ZM3, ZM3C2, ZM3C3, and ZM3C4, respectively. The thin films were subjected to analysis using XRD, SEM, FTIR and UV-vis spectroscopy. The structural and optical parameters of Mg:Cu:ZnO thin films for photonic applications were investigated in detail. The results of the structural and morphological analysis demonstrated that the structural parameters and grain size are dependent on the concentration of dopants. The grain size was calculated to be 55.20, 36.43, 32.64, and 32.57 nm for the ZM3, ZM3C2, ZM3C3, and ZM3C4 films, respectively. The results of the spectroscopy analysis indicated a reduction in the band gap, from 3.9 eV to 3.6 eV, as the concentration of Cu in Mg:Cu:ZnO increased from 0–4%. The optical parameters of the films were obtained through the utilization of FTIR transmission spectrum data and the application of Kramers–Kronig (K-K) relations. The findings indicated that the ZM3C3 film exhibited the highest energy storage capacity and the lowest energy loss when compared to the other samples.