Optical frequency combs offer unprecedented combination of broad bandwidth and high resolution and their coupling to enhancement cavities provides high sensitivity for spectroscopic measurements. Here we use a frequency-comb-based Fourier transform spectrometer (FTS) to measure the narrow resonances of a high-finesse cavity over a bandwidth of 100 nm around 1.55 μm and derive the group delay dispersion (GDD) of the cavity mirrors with precision below 1 fs2 from the cavity resonance frequencies. We do this using a method that allows precise sampling of the comb intensities using an FTS with nominal resolution matched to the comb repetition rate (frep) [1, 2], and we demonstrate that sub-MHz resolution is achieved.