Source identification and accurate measurements of methane gas concentration are key tools necessary for climate change management. Here we present a method for methane isotopologue ratio measurement using a laser-based frequency modulation (FM) spectroscopy technique in the near infrared at 1661 nm. We provide line shape analysis and discuss a fitting algorithm for accurate isotopologue ratio metrology and investigate and minimize the effects of residual amplitude modulation on the experimentally produced FM signal line shape. This FM technique is further evaluated for future development of a cavity-enhanced and noise-immune system capable of isotopologue ratio as well as ultrasensitive trace gas measurements, all accessible using a single distributed feedback laser.