Gas separation and storage are the hot topics for addressing current challenges in energy and environmental science, including the air pollution problems and alternative fuels, and metal–organic frameworks (MOFs) have a great potential in these fields. Herewith, we present the electron paramagnetic resonance (EPR) study of the adsorption of several gases (hydrogen D2, methane 13CH4 and CD4, and carbon dioxide 13CO2) in Cu2+-doped MOF [Zn2(1,4-bdc)2(dabco)]. The obtained compound of composition [Zn1.993Cu0.007(1,4-bdc)2(dabco)] is suitable for studying adsorption geometries at Cu2+ ions and in their closest environments using pulse EPR. In attempt to characterize D2, 13CH4, CD4, and 13CO2 adsorption sites, we applied echo-detected EPR along with hyperfine sublevel correlation spectroscopy and pulse electron-nuclear double resonance spectroscopy. Altogether, these methods demonstrated the preferred location of gas molecules in the framework being at least 6 Å away from the copper ions. In addition, EPR spectroscopy allowed determination of the proton environment of copper and confirmed its incorporation into the MOF lattice, which is hard to establish using other techniques.