Functionalization of quantum carbon dots (QCDs) and graphene quantum dots (GQDs) is a popular way to tune their optical spectra increasing their potential applicability in material science and biorelated disciplines. Based on the experimental observation, functionalization by fluorine atoms induces substantial shifts in absorption and emission spectra and an intensity increase. Understanding of the effects due to fluorine functionalization at the atomic scale level is still challenging due to the complex structure of fluorinated QCDs. In this work, the effect of covalent edge-fluorination and fluorine anion doping on absorption and emission spectra of prototypical polycyclic aromatic hydrocarbons pyrene and circum-pyrene has been investigated. The ways to achieve efficient red-shifts in the UV spectra and obtaining reasonable intensities stood in the focus of the work. High-level quantum chemical methods based on density functional theory/multireference configuration interaction (DFT/MRCI) and single-reference second-order algebraic diagrammatic construction (ADC(2)) and density functional theory (DFT) using the CAM-B3LYP functional have been used for this purpose. The calculations show that doping with the fluoride anion can have significant effects on the electronic spectrum. However, the effect of the fluoride ion is strongly dependent on its position with respect to the QCD. The localization above the GQDs causes large red-shifts to both the absorption and emission of spectra of GQDs, while in-plane localization leads to only negligible shifts and a tendency to dissociation after electronic excitation. Thus, large red-shifts, observed in complexes with F-, are obtained due to the introduction of new excited states with large CT character not yet been considered previously in this context, although they have the potential to significantly influence the photophysics of quantum dots. Doping by edge fluorination redshifts the spectra only slightly. This study provides insights on fluorine-doped GQDs, which is conducive to promoting its rational design and controllable synthesis.