High-resolution broadband direct frequency comb spectroscopy in the mid-infrared spectral region is an extremely powerful and versatile experimental technique that allows study of the molecular structure of gaseous compounds with multiple applicative and scientific implications. Here we present the first implementation of an ultrafast Cr:ZnSe mode-locked laser covering more than 7 THz at around the emission wavelength of 2.4 μm, for direct frequency comb molecular spectroscopy with a frequency sampling of 220 MHz and a frequency resolution of ∼100 kHz. This technique is based on a scanning micro-cavity resonator with a Finesse of ∼12,000 and a diffraction reflecting grating. We demonstrate its application in high-precision spectroscopy of the acetylene molecule by retrieving line center frequencies of more than 68 roto-vibrational lines. Our technique paves the way for real time spectroscopic studies as well as for hyperspectral imaging techniques.