We presented a free-space and multichannel distributed gas sensing method based on optical frequency-modulated continuous-wave (FMCW) interferometry. This method leveraged the FMCW’s capability for the simultaneous acquisition of the absorption path length and gas spectral information, and introduced a differential absorption spectrum scheme. The high ranging resolution of the FMCW guaranteed the measurement accuracy of the absorption path length, and thus ensured the highly precise retrieval of distributed gas concentrations. Furthermore, by exploiting the FMCW’s excellent multiplexing capability, multichannel gas sensing was achieved. In the proof-of-concept experimental demonstration, different concentrations of acetylene gas distributed across three channels with a total of nine monitoring regions were successfully measured. The demonstrated system achieved a ranging resolution of 2 mm and the detection sensitivity of 2 ppm·m. With the advantages of high spectral accuracy, high sensitivity, and high ranging resolution, the proposed method offered a novel approach for the development of distributed spectroscopic gas sensors, targeting challenging applications, such as the monitoring of large-scale gas storage facilities and multi-source industrial gas emissions.