2D hybrid perovskites (2DP) are versatile materials, whose electronic and optical properties can be tuned through the nature of the organic cations (even when those are seemingly electronically inert). Here, it is demonstrated that fluorination of the organic ligands yields glassy 2DP materials featuring long-lived correlated electron-hole pairs. Such states have a marked charge-transfer character, as revealed by the persistent Stark effect in the form of a second derivative in electroabsorption. Modeling shows that electrostatic effects associated with fluorination, combined with the steric hindrance due to the bulky side groups, drive the formation of spatially dislocated charge pairs with reduced recombination rates. This work enriches and broadens the current knowledge of the photophysics of 2DP, which will hopefully guide synthesis efforts toward novel materials with improved functionalities.