Fourier transform spectroscopy based on incoherent light sources is a well-established tool in research fields from molecular spectroscopy and atmospheric monitoring to material science and biophysics. It provides broadband molecular spectra and information about the molecular structure and composition of absorptive media. However, the spectral resolution is fundamentally limited by the maximum delay range ({Delta}$_{max}$) of the interferometer, so acquisition of high-resolution spectra implies long measurement times and large instrument size. We overcome this limit by combining the Fourier transform spectrometer with an optical frequency comb and measuring the intensities of individual comb lines by precisely matching the {Delta}$_{max}$ to the comb line spacing. This allows measurements of absorption lines narrower than the nominal (optical path-limited) resolution without ringing effects from the instrumental lineshape and reduces the acquisition time and interferometer length by orders of magnitude.
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