We report the discovery of two new exoplanet systems around fully convective stars, found from the radial-velocity (RV) variations of their host stars measured with the nIR spectropolarimeter CFHT/SPIRou over multiple years. GJ 3378 b is a planet with minimum mass of 5.26^+0.94^_-0.97_M_{Earth}_ on an eccentric 24.73-day orbit around an M4V star of 0.26M_{sun}_. GJ 1289 b has a minimum mass of 6.27+/-1.25M_{Earth}_ in a 111.74-day orbit, on a circular orbit around an M4.5V star of mass 0.21M_{sun}_. Both stars are in the solar neighbourhood, at 7.73 and 8.86 pc, respectively. The low-amplitude RV signals are detected after line-by-line post-processing treatment. These potential sub-Neptune class planets around cool stars may have temperate atmospheres and be interesting nearby systems for further studies. We also recovered the large-scale magnetic field of both stars, found to be mostly axisymmetric and dipolar, with polar strengths of 20-30G and 200-240G for GJ 3378 (in 2019-21) and GJ 1289 (in 2022-23), respectively. The rotation periods measured with the magnetic field differ from the orbital periods and, in general, stellar activity is not seen in the studied nIR RV time series of both stars. GJ 3378 b detections have not been confirmed by optical RVs and, therefore, they are solely considered a candidate for the present purposes.