We report on the generation of coherent emission from femtosecond (fs) laser-induced filaments mediated by ultrabroadband coherent Raman scattering (CRS), and we investigate its application for high-resolution gas-phase thermometry. Broadband 35-fs, 800-nm pump pulses generate the filament through photoionization of the N₂ molecules, while narrowband picosecond (ps) pulses at 400 nm seed the fluorescent plasma medium via generation of an ultrabroadband CRS signal, resulting in a narrowband and highly spatiotemporally coherent emission at 428 nm. This emission satisfies the phase-matching for the crossed pump-probe beams geometry, and its polarization follows the CRS signal polarization. We perform spectroscopy on the coherent N₂⁺ signal to investigate the rotational energy distribution of the N₂⁺ ions in the excited B²Σ_u⁺ electronic state and demonstrate that the ionization mechanism of the N₂ molecules preserves the original Boltzmann distribution to within the experimental conditions tested.