A statistical treatment is presented of reactive collisions involving N+ ions in the P-3(ja) state with H-2, D-2, and HD molecules in rotation level j of the ground vibration state, leading to either the reaction products H + NH+, D + ND+, and D + NH+ or H + ND+. Unlike previous theoretical work, the fine-structure states of the N+ ions are treated on an equal footing with other internal motions. The calculated cross sections for a given ion energy are averaged over a thermal distribution of initial fine-structure states of N+ for a temperature of 300 K and over a thermal distribution of both the internal rotation states and translation energy of H-2, D-2, and HD for temperatures of 305 and 105 K in order to facilitate a comparison with experiment. The results are presented for a range of collision energies from 10 meV to 1 eV.