  We report the detection and characterization of the transiting sub-Neptune
TOI-1759 b, using photometric time-series from TESS and near infrared
spectropolarimetric data from SPIRou on the CFHT. TOI-1759 b orbits a
moderately active M0V star with an orbital period of $18.849975\pm0.000006$ d,
and we measure a planetary radius and mass of $3.06\pm0.22$ R$_\oplus$ and
$6.8\pm2.0$ M$_\oplus$. Radial velocities were extracted from the SPIRou
spectra using both the CCF and the LBL methods, optimizing the velocity
measurements in the near infrared domain. We analyzed the broadband SED of the
star and the high-resolution SPIRou spectra to constrain the stellar parameters
and thus improve the accuracy of the derived planet parameters. A LSD analysis
of the SPIRou Stokes $V$ polarized spectra detects Zeeman signatures in
TOI-1759. We model the rotational modulation of the magnetic stellar activity
using a GP regression with a quasi-periodic covariance function, and find a
rotation period of $35.65^{+0.17}_{-0.15}$ d. We reconstruct the large-scale
surface magnetic field of the star using ZDI, which gives a predominantly
poloidal field with a mean strength of $18\pm4$ G. Finally, we perform a joint
Bayesian MCMC analysis of the TESS photometry and SPIRou RVs to optimally
constrain the system parameters. At $0.1176\pm0.0013$ au from the star, the
planet receives $6.4$ times the bolometric flux incident on Earth, and its
equilibrium temperature is estimated at $433\pm14$ K. TOI-1759 b is a likely
gas-dominated sub-Neptune with an expected high rate of photoevaporation.
Therefore, it is an interesting target to search for neutral hydrogen escape,
which may provide important constraints on the planetary formation mechanisms
responsible for the observed sub-Neptune radius desert.
