We present the first experimental application of coherent Raman spectroscopy (CRS) on the ro-vibrational ν2 mode spectrum of methane (CH4). Ultrabroadband femtosecond/picosecond (fs/ps) CRS is performed in the molecular fingerprint region from 1100 to 2000 cm-1, employing fs laser-induced filamentation as the supercontinuum generation mechanism to provide the ultrabroadband excitation pulses. We introduce a time-domain model of the CH4 ν2 CRS spectrum, including all five ro-vibrational branches allowed by the selection rules Δv = 1, ΔJ = 0, ±1, ±2; the model includes collisional linewidths, computed according to a modified exponential gap scaling law and validated experimentally. The use of ultrabroadband CRS for in situ monitoring of the CH4 chemistry is demonstrated in a laboratory CH4/air diffusion flame: CRS measurements in the fingerprint region, performed across the laminar flame front, allow the simultaneous detection of molecular oxygen (O2), carbon dioxide (CO2), and molecular hydrogen (H2), along with CH4. Fundamental physicochemical processes, such as H2 production via CH4 pyrolysis, are observed through the Raman spectra of these chemical species. In addition, we demonstrate ro-vibrational CH4 v2 CRS thermometry, and we validate it against CO2 CRS measurements. The present technique offers an interesting diagnostics approach to in situ measurement of CH4-rich environments, e.g., in plasma reactors for CH4 pyrolysis and H2 production.