ABSTRACT This paper analyses spectropolarimetric observations of the classical T Tauri star (CTTS) GM Aurigae collected with SPIRou, the near-infrared spectropolarimeter at the Canada–France–Hawaii Telescope, as part of the SLS and SPICE Large Programs. We report for the first time results on the large-scale magnetic field at the surface of GM Aur using Zeeman Doppler imaging. Its large-scale magnetic field energy is almost entirely stored in an axisymmetric poloidal field, which places GM Aur close to other CTTSs with similar internal structures. A dipole of about 730 G dominates the large-scale field topology, while higher order harmonics account for less than 30 per cent of the total magnetic energy. Overall, we find that the main difference between our three reconstructed maps (corresponding to sequential epochs) comes from the evolving tilt of the magnetic dipole, likely generated by non-stationary dynamo processes operating in this largely convective star rotating with a period of about 6 d. Finally, we report a $5.5\sigma$ detection of a signal in the activity-filtered radial velocity data of semi-amplitude $110\pm 20$ m s$^{-1}$ at a period of $8.745\pm 0.009$ d. If attributed to a close-in planet in the inner accretion disc of GM Aur, it would imply that this planet candidate has a minimum mass of $1.10 \pm 0.30\, M_\mathrm{Jup}$ and orbits at a distance of $0.082 \pm 0.002$ au.