We present a fast-scanning Fourier transform spectrometer (FTS) in combination with high-repetition-rate mid-infrared supercontinuum sources, covering a wavelength range of 2-10.5 µm. We demonstrate the performance of the spectrometer for trace gas detection and compare various detection methods: baseband detection with a single photodetector, baseband balanced detection, and synchronous demodulation at the repetition rate of the supercontinuum source. The FTS uses off-the-shelf optical components and provides a minimum spectral resolution of 750 MHz. It achieves a noise equivalent absorption sensitivity of ∼10-6 cm-1 Hz-1/2 per spectral element, by using a 31.2 m multipass absorption cell.