Chirped laser dispersion spectroscopy (CLaDS) is a sensitive and robust method for gas detection. In CLaDS, a multitone laser beam is sent through the sample and focused onto the detector where RF beat note is generated. Spectroscopic information is subsequently retrieved through frequency demodulation of this beat note. When CLaDS is used for open-path sensing (i.e., when the pressure-broadened transitions are measured), demodulation at high frequency is required (1 GHz and beyond). We address this issue with a parametric downconversion of the beat note signal. This approach moves CLaDS toward compact, cheaper, and more robust implementations and can be used in both near- and mid-infrared regions. A setup operating at 1650 nm is presented and characterized. Ambient methane detection with an open-path multipass cell is demonstrated.