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In this Letter, we present a method of performing broadband mid-infrared spectroscopy with conventional, free-running, continuous wave Fabry-Perot quantum cascade lasers (FP-QCLs). The measurement method is based on multi-heterodyne down-conversion of optical signals. The sample transmission spectrum probed by one multi-mode FP-QCL is down-converted to the radio-frequency domain through an optical multi-heterodyne process using a second FP-QCL as the local oscillator. Both a broadband multi-mode spectral measurement as well as high-resolution (∼15 MHz) spectroscopy of molecular absorption are demonstrated and show great potential for development of high performance FP-laser-based spectrometers for chemical sensing.