Existence of minimizers for the Dirac-Fock model for crystals was recently proved by Paturel and Séré and the authors [9]. In this paper, inspired by Ghimenti and Lewin's result [12] for the periodic Hartree-Fock model, we prove that the Fermi level of any periodic Dirac-Fock minimizer is either empty or totally filled when α/c\leq C_{cri} and α > 0. Here c is the speed of light, α is the fine structure constant, and C cri is a constant only depending on the number of electrons and on the charge of nuclei per cell. More importantly, we provide an explicit upper bound for C_{cri} .Our result implies that any minimizer of the periodic Dirac-Fock model is a projector when α/c\leq C_{cri} and α > 0 In particular, the non-relativistic regime (i.e., c >>1) and the weak coupling regime (i.e., 0< α <<1) are covered.The proof is based on a delicate study of a second-order expansion of the periodic Dirac-Fock functional composed with a retraction that was introduced by Séré in [23] for atoms and molecules and later extended to the case of crystals in.