The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the standard lore. I present a mechanism for superconductivity in low-density three-dimensional Dirac materials that are close to a ferroelectric quantum critical point. I show that while the Coulomb repulsion between electrons is strongly screened by the lattice polarization near the critical point, the electron-phonon coupling is significantly increased by critical fluctuations, even in the case of vanishing carrier density. Applying these results to low-density systems, I show that the superconducting transition temperature is strongly enhanced upon approaching the quantum critical point. Furthermore, I will demonstrate that at vanishing electron density the ferroelectric transition is preempted by a new ferroelectric density wave order, which breaks translational symmetry in addition to inversion. This new quantum critical point significantly enhances soft phonon fluctuations, resulting in a strong pairing interaction that can drive a superconducting instability even at vanishing carrier density.