The dissociative recombination and excitation of CF+ have been measured at the ASTRID and CRYRING storage rings. Though examination of the available potential energy curves would suggest that the recombination rate would be large for this ion, in fact a rate constant of 5.2 +/- 1.0 x 10(-8) (T-e/300)(-0.8) cm(3) s(-1) was found. The recombination cross section at low energies falls off to a minimum at 0.5 eV centre-of-mass collision energy but exhibits resonances at energies above this. The dissociative excitation cross section leading to C+ + F was also measured and this displays an onset beginning at about 7 eV.