  The space environment in which planets are embedded depends mainly on the
host star and impacts the evolution of the planetary atmosphere. The quiet M
dwarf GJ 436 hosts a close-in hot Neptune which is known to feature a
comet-like tail of hydrogen atoms escaped from its atmosphere due to energetic
stellar irradiation. Understanding such star-planet interactions is essential
to shed more light on planet formation and evolution theories, in particular
the scarcity of Neptune-size planets below 3 d orbital period, also known as
``Neptune desert''. We aimed at characterising the stellar environment around
GJ 436, which requires an accurate knowledge of the stellar magnetic field. The
latter is studied efficiently with spectropolarimetry, since it is possible to
recover the geometry of the large-scale magnetic field by applying tomographic
inversion on time series of circularly polarised spectra. We used
spectropolarimetric data collected in the optical domain with Narval in 2016 to
compute the longitudinal magnetic field, examine its periodic content via
Lomb-Scargle periodogram and Gaussian Process Regression analysis, and finally
reconstruct the large-scale field configuration by means of Zeeman-Doppler
Imaging. We found an average longitudinal field of -12 G and a stellar rotation
period of 46.6 d using a Gaussian Process model and 40.1 d using Zeeman-Doppler
Imaging, both consistent with the literature. The Lomb-Scargle analysis did not
reveal any significant periodicity. The reconstructed large-scale magnetic
field is predominantly poloidal, dipolar and axisymmetric, with a mean strength
of 16 G. This is in agreement with magnetic topologies seen for other stars of
similar spectral type and rotation rate.
