  We present near-infrared spectropolarimetric observations of a sample of 43
weakly- to moderately-active M dwarfs, carried with SPIRou at the
Canada-France-Hawaii Telescope in the framework of the SPIRou Legacy Survey
from early 2019 to mid 2022. We use the 6700 circularly polarised spectra
collected for this sample to investigate the longitudinal magnetic field and
its temporal variations for all sample stars, from which we diagnose, through
quasi-periodic Gaussian process regression, the periodic modulation and
longer-term fluctuations of the longitudinal field. We detect the large-scale
field for 40 of our 43 sample stars, and infer a reliable or tentative rotation
period for 38 of them, using a Bayesian framework to diagnose the confidence
level at which each rotation period is detected. We find rotation periods
ranging from 14 to over 60d for the early-M dwarfs, and from 70 to 200d for
most mid- and late-M dwarfs (potentially up to 430d for one of them). We also
find that the strength of the detected large-scale fields does not decrease
with increasing period or Rossby number for the slowly rotating dwarfs of our
sample as it does for higher-mass, more active stars, suggesting that these
magnetic fields may be generated through a different dynamo regime than those
of more rapidly rotating stars. We also show that the large-scale fields of
most sample stars evolve on long timescales, with some of them globally
switching sign as stars progress on their putative magnetic cycles.
