Time-domain spectroscopy using dual, coherent frequency combs is used to measure free-induction decay from a molecular gas sample in the near-IR with a time-domain signal-to-noise ratio of approximately 10(6) over a approximately 6 ns window at 55 fs time resolution (corresponding to the 9 THz source bandwidth) and a frequency/timing accuracy set by the frequency combs. The free-induction decay exhibits the expected periodic pulses from the rephasing of the multiply excited rovibrational levels. This demonstration represents the first high-resolution, high-accuracy, broadband measurement of optical free-induction decay, to our knowledge.