The structural and spectroscopic parameters of the fluorine doped carbon isomers, CnF2+ (n = 1-5) cations, were calculated using frozen core second order Moller-Plesset perturbation theory (MP2(fc)) at the complete basis set (CBS) limit with the aug-cc-pVXZ (X = D, T, Q) basis sets. The optimised geometries, rotational constants, dipole moments, and vibrational frequencies of the cations were computed to the CBS limit. The even-odd alternation effect was observed in the geometrical parameters, the dipole moments and the stabilities of the isomers. The carbon clusters containing even numbers of carbon atoms are linear with D-infinity h symmetry, while those containing an odd number of carbon atoms adopt a bent structure with bond angle in the range 120-130 degrees. Some of the calculated parameters show good agreement to those available in the literature. Therefore, the reported data of the isomers should be accurate and it is hoped that the data on the isomers will be useful in helping to detect these cations in the interstellar medium.