We report results of a spectropolarimetric and photometric monitoring of the weak-line T Tauri star V410 Tau based on data collected mostly with SPIRou, the near-infrared (NIR) spectropolarimeter recently installed at the Canada-France-Hawaii Telescope, as part of the SPIRou Legacy Survey large programme, and with TESS between October and December 2019. Using Zeeman-Doppler Imaging (ZDI), we obtained the first maps of photospheric brightness and large-scale magnetic field at the surface of this young star derived from NIR spectropolarimetric data. For the first time, ZDI is also simultaneously applied to high-resolution spectropolarimetric data and very-high-precision photometry. V410 Tau hosts both dark and bright surface features and magnetic regions similar to those previously imaged with ZDI from optical data, except for the absence of a prominent dark polar spot. The brightness distribution is significantly less contrasted than its optical equivalent, as expected from the difference in wavelength. The large-scale magnetic field (∼410 G), found to be mainly poloidal, features a dipole of ∼390 G, again compatible with previous studies at optical wavelengths. NIR data yield a surface differential rotation slightly weaker than that estimated in the optical at previous epochs. Finally, we measured the radial velocity of the star and filtered out the stellar activity jitter using both ZDI and Gaussian Process Regression down to a precision of ∼0.15∼ and 0.08 km/s RMS, respectively, confirming the previously published upper limit on the mass of a potential close-in massive planet around V410 Tau.