  By using Bismut's approach about the Malliavin calculus with jumps, we study
the regularity of the distributional density for SDEs driven by degenerate
additive L\'evy noises. Under full H\"ormander's conditions, we prove the
existence of distributional density and the weak continuity in the first
variable of the distributional density. Under the uniform first order Lie's
bracket condition, we also prove the smoothness of the density.
