A new approach is described to compensate the variations induced by laser frequency instabilities in the recently demonstrated Fourier transform spectroscopy that is based on the RF beating spectra of two frequency combs generated by mode-locked lasers. The proposed method extracts the mutual fluctuations of the lasers by monitoring the beating signal for two known optical frequencies. From this information, a phase correction and a new time grid are determined that allow the full correction of the measured interferograms. A complete mathematical description of the new active spectroscopy method is provided. An implementation with fiberbased mode-locked lasers is also demonstrated and combined with the correction method a resolution of 0.067 cm(-1) (2 GHz) is reported. The ability to use slightly varying and inexpensive frequency comb sources is a significant improvement compared to previous systems that were limited to controlled environment and showed reduced spectral resolution. The fast measurement rate inherent to the RF beating principle and the ease of use brought by the correction method opens the venue to many applications.