GRBs produced by the collapse of massive stars are usually found near the most prominent star-forming regions of star-forming galaxies. GRB 171205A happened in the outskirts of a spiral galaxy, a peculiar location in an atypical GRB host. In this paper we present a highly-resolved study of the molecular gas of this host, with CO(1-0) observations from ALMA. We compare with GMRT atomic HI observations, and with data at other wavelengths to provide a broad-band view of the galaxy. The ALMA observations have a spatial resolution of 0.2" and a spectral resolution of 10 km/s, observed when the afterglow had a flux density of ~53 mJy. This allowed a molecular study both in emission and absorption. The HI observations allowed to study the host galaxy and its extended environment. The CO emission shows an undisturbed spiral structure with a central bar, and no significant emission at the location of the GRB. Our CO spectrum does not reveal any CO absorption, with a column density limit of < 10^15 cm^-2. This argues against the progenitor forming in a massive molecular cloud. The molecular gas traces the galaxy arms with higher concentration in the regions dominated by dust. The HI gas does not follow the stellar light or the molecular gas and is concentrated in two blobs, with no emission towards the centre of the galaxy, and is slightly displaced towards the southwest of the galaxy, where the GRB exploded. Within the extended neighbourhood of the host galaxy, we identify another prominent HI source at the same redshift, at a projected distance of 188 kpc. Our observations show that the progenitor of this GRB is not associated to a massive molecular cloud, but more likely related to low-metallicity atomic gas. The distortion in the HI gas field is indicator of an odd environment that could have triggered star formation and could be linked to a past interaction with the companion galaxy.

13 pages, 10 figures, 8 tables, A&A submitted after 1st referee review