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The detection of CF$^+$ in interstellar clouds potentially allows astronomers to infer the elemental fluorine abundance and the ionization fraction in ultraviolet-illuminated molecular gas. Because local thermodynamic equilibrium (LTE) conditions are hardly fulfilled in the interstellar medium (ISM), the accurate determination of the CF$^+$ abundance requires one to model its non-LTE excitation via both radiative and collisional processes. Here, we report quantum calculations of rate coefficients for the rotational excitation of CF$^+$ in collisions with para- and ortho-H2 (for temperatures up to 150 K). As an application, we present non-LTE excitation models that reveal population inversion in physical conditions typical of ISM photodissociation regions (PDRs). We successfully applied these models to fit the CF$^+$ emission lines previously observed toward the Orion Bar and Horsehead PDRs. The radiative transfer models achieved with these new rate coefficients allow the use of CF$^+$ as a powerful probe to study molecular clouds exposed to strong stellar radiation fields.