Physisorption of H2 by nanoporous materials is among the most technologically promising hydrogen storage techniques. Classical-fluid density functional theory (DFT) is commonly used for rapid estimation of the adsorption free energies. For the light hydrogen guest, quantum effects may also become important. Following Kohn-Sham partitioning scheme, we develop quantized extension of the molecular-fluid DFT. The ingredients of the technique are the kinetic energy of quantized ideal gas, the mean-field interaction potential, and the excess free energy functional. The functional is constructed to reproduce the experimental equation of state, and the density profiles of the classical hydrogen adsorbed in a slit pore. We consider two functional forms of the free-energy functionals: the local-interaction expression (LIE) approximation, and the scaled-density approximation (SDA). The LIE functional reproduces adsorption thermodynamics in open pores, but not the microscopic fluid structure. The non-local SDA functional corrects this deficiency, but still fails for isolated adsorption sites.