The direct oxidation of methane to methanol (DOMTM) remains challenging due to the low reactivity of methane and difficulties in achieving high activity and selectivity under mild conditions. In this work, Cu-ZSM-5 catalysts were systematically investigated using H2O2 as oxidant in water at 50 °C to establish quantitative structure–activity relationships. Comprehensive characterization of copper speciation, dispersion, acidity, and framework aluminum coordination was performed. Preservation of the MFI structure was confirmed by X-ray diffraction, while Brønsted and Lewis acid sites were quantified using pyridine adsorption, and framework and extra-framework aluminum coordination was determined by 27Al solid-state NMR. Copper dispersion, quantified by N2O oxidation–H2 reduction (TPR), along with UV–Vis diffuse reflectance spectroscopy and H2-TPR, indicated the presence of isolated Cu2+ species. Turnover frequency exhibited non-monotonic dependencies on Brønsted acid site density and BAS/LAS ratio. Methanol formation was maximized (productivity of 750 μmol g−1 h−1 with a selectivity of 49% to methanol) within Brønsted acid site densities of 0.58–0.96 μmol m−2 and BAS/LAS ratios of 1.0–1.7, highlighting the synergistic effect of BAS-LAS pairs. These results demonstrate that high methanol productivity arises from a cooperative interplay between copper dispersion, acid site density, and BAS-LAS synergy. Rigorous quantification of all oxidation products (CH3OOH, CH3OH, HCHO, HCOOH, CO2) enabled accurate evaluation of catalytic performance under low-conversion conditions.