Modulating the signal is a common method in spectroscopy for reducing noise. However, for broadband coherent light sources like optical frequency combs (OFCs), modulation methods typically involve the use of optical modulators, making the experimental setup cumbersome. This study proposes and successfully implements a broadband Faraday modulation rotation spectroscopy (FAMOS) method combined with an OFC. The development of this method by extending the modulation frequency of the OFC from tens of MHz down to the kHz level, effectively relaxes the stringent demands for high-speed electronics and optoelectronic devices, making modulation spectroscopy techniques more practically useful for diverse real-world environments. Moreover, through specifically designed modulation strategies, this method can effectively suppress low-frequency noise, thereby significantly improving the signal-to-noise ratio of the measurements without sacrificing measurement accuracy.