  We present a group theoretical and ab-initio analysis of lattice point
defects in fluorographene, with a focus on neutral and negative
$\text{V}_{\text{CF}}$ vacancies. By using a combination of density functional
theory calculations and group theory analysis, we investigate the many-body
configurations of the defects and calculate the vertical absorption and
zero-phonon line energies of the excited states and their dependence with
strain. The description of the defects is extended by computing their formation
energy, as well as further relevant parameters as the Jahn-Teller energy for
neutral $\text{V}_{\text{CF}}$ and the zero field splitting for negative
$\text{V}_{\text{CF}}$ vacancies. Based on our results, we discuss possible
quantum applications of these color centers when coupled to mechanical
oscillation modes of the hosting two-dimensional material. The symmetry and
active orbitals of the defects exhibit a parallelism with those of the
extensively studied NV centers in diamond. In this context, the studied defects
emerge as interesting candidates for the development of two-dimensional quantum
devices based on fluorographene.
