A theoretical method of studying the effect of weak shape anisotropy on the freezing properties of classical fluids is discussed. A choice of an appropriate reference isotropic potential for a given general anisotropic model leads to the separation of the free energy into the part due to lattice formation, and the orientational correction. The reference free energy is calculated by applying the density functional theory. The anisotropic contribution to the free energy is treated by a self-consistent theory of orientational order. As an application, fluid-solid equilibria in the hard dumbbell model are considered. For the plastic crystal and the orientationally ordered phases of the hard dumbbell model, appropriate choices are made for the isotropic reference potential, density functional method is applied, and the resulting translational distribution of the molecular centers are utilized in the self-consistent calculation of the orientational ordering in the solid. The results obtained for the hard dumbbell fluids with various anisotropies are compared with the existing simulation data.