We present results from our recent studies of the dissociative recombination of the CF⁺ cation. On one hand, dissociative recombination was measured with 3 MeV CF⁺ ions in the heavy-ion Test Storage Ring in Heidelberg, using the twin electron beam configuration with an electron cooler and a separated electron target for collision measurements. In this experiment, the low temperatures of the electron beam provided by a photocathode (temperature in co-moving frame below 1 meV) account for a fast kinetic cooling of the heavy-ion beam and a high resolution in the measured rate coefficients. Fragment imaging measurements show a complete switching of the dissociation route by only a small change of the collision energy and the disappearance of neutral Rydberg product states on crossing the DE threshold. On the other hand, extensive calculations of energy positions and autoionization widths for the doubly excited states of CF between the first and second ionization thresholds have been obtained from electron scattering calculations using the complex Kohn variational method, followed by calculations of the dissociative recombination process with the multichannel quantum defect theory. In preliminary computations, only the first dissociative state in each molecular symmetry, which lies closest in energy to the ion potential at its equilibrium internuclear separation, and thus is dominant for the low-energy dissociative recombination, was included. Although only the direct mechanism of dissociative recombination reaction has been considered in this step, the size and the shape of the DR rate coefficient are already well reproduced.