Classical density functional theory is used to determine the fluid-solid surface tensions for low-index faces of crystals of hard spheres and Lennard-Jones particles. The calculations make use of the recently introduced explicitly stable fundamental measure theory model for hard spheres, and we show that this gives state-of-the-art accuracy compared to simulation. For the Lennard-Jones system, results are presented for both solid-liquid and solid-vapor interfaces, and in both cases the FCC results compare favorably with existing results from the literature. We find that the BCC crystal has significantly lower solid-liquid surface tension than the FCC structure. For the solid-vapor interface, our results indicate that the BCC phase is unstable with respect to transition to the HCP structure, in agreement with various zero-temperature results in the literature.