We present broadband, dual-pump coherent anti-Stokes Raman scattering (CARS) measurements of N2 and O2 in 2m diameter methanol pool fires. The design of the fiber-optically coupled CARS instrument for fire measurements is described. Single-shot temperatures and O2/N2 ratios were obtained simultaneously from a single measurement point at the center of the fire plume, and the measured temperature-oxygen statistics are compared to results of a time-domain-filtered Reynolds-averaged Navier-Stokes simulation. The measured and simulated mean fire temperatures agree to within 2-4%, with larger turbulent fluctuations observed in the measured temperatures. The behavior of the mean temperature conditioned on the O2/N2 ratio is similar for both simulation and experiment, but with simulated temperatures that are up to 10% lower than measured values for O2/N2 below 0.18. The uncertainty in the CARS measurements is described. A single-shot detection limit of O2/N2=0.06 was determined from the observed signal to noise ratio in the measured O2 Q-branch spectra. Comparison of the CARS and thermocouple-measured temperatures in tube-furnace-heated air allowed characterization of the CARS instrument accuracy and precision and it was determined that between 500-1400K the instrument accuracy is 1% and the measurements are reproducible to within 5-7%.