  As a potent greenhouse gas and ozone depleting agent, nitrous oxide (N$_2$O)
plays a critical role in the global climate. Effective mitigation relies on
understanding global sources and sinks which can be supported through isotopic
analysis. We present a cross-dispersed spectrometer, coupled with a
mid-infrared frequency comb, capable of simultaneously monitoring all singly
substituted, stable isotopic variants of N$_2$O. Rigorous evaluation of the
instrument lineshape function and data treatment are discussed. Laboratory
characterization of the spectrometer demonstrates sub-GHz spectral resolution
and an average precision of $7.4\times10^{-6}$ for fractional isotopic
abundance retrievals in 1 s.
