In storage rings, short electron bunches can produce an intense THz radiation called Coherent Synchrotron Radiation (CSR). The flux of this emission between 250 and 750 GHz is very advantageous for spectroscopy, but intensity fluctuations lead to artifacts in the FTIR spectra and, until now, prevented the use of CSR for high-resolution measurements. At SOLEIL, we found stable CSR conditions for which the signal-to-noise ratio (S/N) allows for measurements at high resolution. Moreover, we developed an artifact correction system, based on a simultaneous detection of the input and the output signals of the interferometer, which allows improving further the signal-to-noise ratio. The stable CSR combined with this ingenious technique allowed us to record for the first time high-resolution FTIR spectra in the sub-THz range, with an exceptional S/N of 100 in a few hours.