An analytic approach is used to evaluate how the angular structure of a molecular fluid contributes to its thermodynamic properties, The average interactions (energy, forces, etc.) between molecules are first expressed as integrals over a spherical-harmonic expansion of the pair distribution function of the fluid. Angularly averaged interactions for systems described by site-site representations of the intermolecular potentials are then developed. Specifically, homonuclear diatomic molecules described by two-site potential are considered in this paper. These results are used to examine the role that fluid structure plays in determining the average energy, pressure, and forces on a molecule, using as comparison simulation data on dense, fluid nitrogen.