Context. CF+ has recently been detected in the Horsehead and Orion Bar photo-dissociation regions. The J = 1−0 line in the Horsehead is double-peaked in contrast to other millimeter lines. The origin of this double-peak profile may be kinematic or spectroscopic. Aims. We investigate the effect of hyperfine interactions due to the fluorine nucleus in CF + on the rotational transitions. Methods. We compute the fluorine spin rotation constant of CF + using high-level quantum chemical methods and determine the relative positions and intensities of each hyperfine component. This information is used to fit the theoretical hyperfine components to the observed CF + line profiles, thereby employing the hyperfine fitting method in GILDAS. Results. The fluorine spin rotation constant of CF + is 229.2 kHz. This way, the double-peaked CF + line profiles are well fitted by the hyperfine components predicted by the calculations. The unusually large hyperfine splitting of the CF + line therefore explains the shape of the lines detected in the Horsehead nebula, without invoking intricate kinematics in the UV-illuminated gas.