This study presents the fabrication and characterization of pure and copper doped zinc oxide (Cu-doped ZnO) thin films with varying copper concentrations. The films were synthesized using co-precipitation and spin coating methods, followed by post-annealing at 450 °C for 6 h in ambient air. Structural and optical properties of the samples were analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray (EDX) spectroscopy, ultraviolet–visible (UV–Vis) spectroscopy, Fourier transform infrared (FTIR) spectroscopy, and Raman spectroscopy. Structural analysis revealed a decrease in average crystalline size up to 2 wt% copper doping, followed by an increase with higher doping concentrations. SEM micrographs supported these findings. The band gap of the samples narrowed with increasing copper doping, from approximately 3.22 eV for pure ZnO to 2.72 eV for the 6 wt% copper doped sample. Furthermore, frequency variations in the 400–600 cm−1 wavelength interval were observed in the FTIR vibrational bands of zinc oxide due to increasing copper doping.