  In this paper we present an analysis of near-infrared spectropolarimetric and
velocimetric data of the young M dwarf AU Mic, collected with SPIRou at the
Canada-France-Hawaii telescope from 2019 to 2022, mostly within the SPIRou
Legacy Survey. With these data, we study the large- and small-scale magnetic
field of AU Mic, detected through the unpolarized and circularly-polarized
Zeeman signatures of spectral lines. We find that both are modulated with the
stellar rotation period (4.86 d), and evolve on a timescale of months under
differential rotation and intrinsic variability. The small-scale field,
estimated from the broadening of spectral lines, reaches $2.61\pm0.05$ kG. The
large-scale field, inferred with Zeeman-Doppler imaging from Least-Squares
Deconvolved profiles of circularly-polarized and unpolarized spectral lines, is
mostly poloidal and axisymmetric, with an average intensity of $550\pm30$ G. We
also find that surface differential rotation, as derived from the large-scale
field, is $\simeq$30% weaker than that of the Sun. We detect the radial
velocity (RV) signatures of transiting planets b and c, although dwarfed by
activity, and put an upper limit on that of candidate planet d, putatively
causing the transit-timing variations of b and c. We also report the detection
of the RV signature of a new candidate planet (e) orbiting further out with a
period of $33.39\pm0.10$ d, i.e., near the 4:1 resonance with b. The RV
signature of e is detected at 6.5$\sigma$ while those of b and c show up at
$\simeq$4$\sigma$, yielding masses of $10.2^{+3.9}_{-2.7}$ and
$14.2^{+4.8}_{-3.5}$ Earth masses for b and c, and a minimum mass of
$35.2^{+6.7}_{-5.4}$ Earth masses for e.
