Analytical approximations for the pair direct correlation function (DCF) of molecular fluids and their mixtures are derived within the frame of a new formalism based on weighted density functional methods which represents a generalization of Rosenfeld theory for hard spheres mixtures [J. Chem. Phys. 89, 4271 (1988)]. These approximations rest upon the geometrical properties of individual molecules such as the volume, the surface, and the mean radius. They are Percus-Yevick (PY) like in nature and reduce to the analytical PY solution for DCF in the hard sphere case. By construction the approximations incorporate several interesting features : They yield the Mayer function in the low density limit as expected, and they are anisotropic at zero separation as well as at contact. In addition they predict an orientational instability of the isotropic phase with respect to the nematic phase, a feature that is absent from the Percus-Yevick theory. Comparisons are made with the Percus-Yevick numerical results for the DCF for various convex hard bodies such as hard ellipsoids of revolutions (prolate and oblate), prolate spherocylinders, cutspheres, and generally the agreement is very good for a large range of liquid densities. Analytical expressions for the virial and compressibility routes for the pressures are also given. The results obtained for a large varieties of convex bodies are in very good agreement with corresponding numerical Percus-Yevick results. These approximations can be generalized to inhomogeneous systems in a straightforward manner.