The two-point correlation function of inhomogeneous hard sphere fluids is analyzed within a certain version of weighted density functional theory. We have determined the direct correlation function and, based on the Ornstein-Zernicke equation, its inverse, yielding the structure factor for such fluids confined by hard, structureless, and parallel walls. We have also calculated the excess coverage and the finite size contribution to the free energy as a function of the slit width L for various bulk densities. In quantitative agreement with rigorous results, the present version of density functional theory yields a constant and large but finite number density profile in the slit for the limiting case that L is reduced to the diameter of the hard spheres. (C) 1998 Elsevier Science B.V. All rights reserved.