  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 $\mathrm{km\,s^{-1}}$
RMS, respectively, confirming the previously published upper limit on the mass
of a potential close-in massive planet around V410 Tau.
