Accurate parameters of molecular transitions are needed for data analysis in many applications, ranging from atmospheric research to astrophysics and determination of fundamental constants. Optical frequency comb Fourier transform spectroscopy (OFC-FTS) is particularly well-suited for high-precision measurements of broadband molecular spectra. From these spectra, the parameters of individual transitions - all measured simultaneously under the same experimental conditions - can be determined. We use a mechanical OFC-FTS spectrometer with sub-nominal resolution [1, 2] to perform precise broadband measurements of entire molecular bands of CO2 using either direct absorption spectroscopy or cavity-enhanced complex refractive index spectroscopy (CE-CRIS) [3] and we extract line parameters for line shapes beyond the Voigt profile.