  We describe advances on a method designed to derive accurate parameters of M dwarfs. Our analysis consists in comparing high-resolution infrared spectra acquired with the near-infrared spectro-polarimeter SPIRou to synthetic spectra computed from MARCS model atmospheres, in order to derive the effective temperature ($T_{\rm eff}$), surface gravity ($\rm \log{g}$), metallicity ([M/H]) and alpha-enhancement ($\rm [\alpha/Fe]$) of 44 M dwarfs monitored within the SPIRou Legacy Survey (SLS). Relying on 12 of these stars, we calibrated our method by refining our selection of well modelled stellar lines, and adjusted the line list parameters to improve the fit when necessary. Our retrieved $T_{\rm eff}$, $\rm \log{g}$ and [M/H] are in good agreement with literature values, with dispersions of the order of 50 K in $T_{\rm eff}$ and 0.1 dex in $\rm \log{g}$ and [M/H]. We report that fitting $\rm [\alpha/Fe]$ has an impact on the derivation of the other stellar parameters, motivating us to extend our fitting procedure to this additional parameter. We find that our retrieved $\rm [\alpha/Fe]$ are compatible with those expected from empirical relations derived in other studies. 
Estimating the atmospheric properties of 44 M dwarfs from SPIRou spectra