  We present the results of a study aiming at retrieving the fundamental
parameters of M dwarfs from spectra secured with SPIRou, the near-infrared
high-resolution spectropolarimeter installed at the Canada-France-Hawaii
Telescope (CFHT), in the framework of the SPIRou Legacy Survey (SLS). Our study
relies on comparing observed spectra with two grids of synthetic spectra,
respectively computed from PHOENIX and MARCS model atmospheres, with the
ultimate goal of optimizing the precision at which fundamental parameters can
be determined. In this first step, we applied our technique to 12 inactive M
dwarfs with effective temperatures ($T_{\rm eff}$) ranging from 3000 to 4000 K.
We implemented a benchmark to carry out a comparison of the two models used in
this study. We report that the choice of model has a significant impact on the
results and may lead to discrepancies in the derived parameters of 30 K in
$T_{\rm eff}$ and 0.05 dex to 0.10 dex in surface gravity ($\log{g}$) and
metallicity ([M/H]), as well as systematic shifts of up to 50 K in $T_{\rm
eff}$ and 0.4 dex $\log{g}$ and [M/H]. The analysis is performed on high
signal-to-noise ratio template SPIRou spectra, averaged over multiple
observations corrected from telluric absorption features and sky lines, using
both a synthetic telluric transmission model and principal component analysis.
With both models, we retrieve $T_{\rm eff}$ , $\log{g}$ and [M/H] estimates in
good agreement with reference literature studies, with internal error bars of
about 30 K, 0.05 dex and 0.1 dex, respectively.
