High-speed Raman spectroscopy has become increasingly important for analyzing chemical dynamics in real time. To address the need, rapid-scan Fourier-transform coherent anti-Stokes Raman scattering (FT-CARS) spectroscopy has been developed to realize broadband CARS measurements at a scan rate of more than 20,000 scans/s. However, the detection sensitivity of FT-CARS spectroscopy is inherently low ... [Show full abstract] due to the limited number of photons detected during each scan. In this Letter, we show our experimental demonstration of enhanced sensitivity in rapid-scan FT-CARS spectroscopy by heterodyne detection. Specifically, we implemented heterodyne detection by superposing the CARS electric field with an external local oscillator (LO) for their interference. The CARS signal was amplified by simply increasing the power of the LO without the need for increasing the incident power onto the sample. Consequently, we achieved enhancement in signal intensity and the signal-to-noise ratio by factors of 39 and 5, respectively, compared to FT-CARS spectroscopy with homodyne detection. The sensitivity-improved rapid-scan FT-CARS spectroscopy is expected to enable the sensitive real-time observation of chemical dynamics in a broad range of settings, such as combustion engines and live biological cells.