The generalized van der Waals free energy density functional formalism of inhomogeneous fluids has been applied to study the thermodynamics and structural properties of a system of identical charged hard spheres neutralized by a uniform penetrating background. Nonlocal entropic effects are included through a simple density independent coarse-graining kernel and the hard-sphere truncation of the Coulomb interaction in the ionic atmosphere is accounted for within a mean-field approximation. In the first instance a parametric charge density of known form is introduced yielding essentially analytic results. Second, the functional is optimized with full variational flexibility to produce a theory directly analogous with the Poisson–Boltzmann approach to Coulomb fluids. A linearized version corresponding to a Debye–Hückel approximation is also discussed. The results compare favorably with Monte Carlo simulation in the regime of low to intermediate bulk density. At high volume fractions (>0.1) the functional becomes ill conditioned as the excluded volume effect is exaggerated and the mean-field hole correction fails to account for the hard-sphere structure.