Abstract: Direct-comb spectroscopy techniques uses optical frequency combs (OFCs) as spectroscopic light source. They deliver high sensitivity, high frequency resolution and precision in a broad spectral range. Due to these features, the field has burgeoned in recent years. In this work we constructed an OFC-based cavity-enhanced Fourier-transform spectrometer in the near-infrared region and used it for a line-shape study of rovibrational transitions of CO perturbed by Ar. The highly sensitive measurements spanned the wavenumber range from 6270 cm^-1 to 6410 cm^-1, which covered both P and R branch of the second overtone band of CO. The spectrometer delivers high-resolution surpassing the Fourier-transform resolution limit determined by interferogram length, successfully removing ringing and broadening effects caused by instrumental line shape function. The instrumental-line-shape-free method and high signal-to-noise ratio in the measurement allowed us to observe collisional effects beyond those described by the Voigt profile. We retrieved collisional line-shape parameters by fitting the speed-dependent Voigt profile and found good agreement with the values given by precise cavity ring-down spectroscopy measurements that used a continuous-wave laser referenced to a stabilized OFC. The results demonstrate that OFC-based cavity-enhanced Fourier-transform spectroscopy is a strong tool for accurate line-shape studies that will be crucial for future spectral databases.