Context. Atomic gas in the diffuse interstellar medium (ISM) is organized in filamentary structures. These structures usually host cold and dense molecular clumps. The Galactic magnetic field is considered to play an important role in the formation of these clumps. Aims. Our goal is to explore the role of the magnetic field in the H_I-H₂ transition process. Methods. We targeted a diffuse ISM filamentary cloud toward the Ursa Major cirrus where gas transitions from atomic to molecular. We probed the magnetic field properties of the cloud with optical polarization observations. We performed multiwavelength spectroscopic observations of different species in order to probe the gas phase properties of the cloud. We observed the CO (J = 1−0) and (J = 2−1) lines in order to probe the molecular content of the cloud. We also obtained observations of the [C ii] 157.6µm emission line in order to trace the CO-dark H₂ gas and estimate the mean volume density of the cloud. Results. We identified two distinct subregions within the cloud. One of the regions is mostly atomic, while the other is dominated by molecular gas, although most of it is CO-dark. The estimated plane-of-the-sky magnetic field strength between the two regions remains constant within uncertainties and lies in the range 13–30 µG. The total magnetic field strength does not scale with density. This implies that gas is compressed along the field lines. We also found that turbulence is trans-Alfvénic, with M_A ≈ 1. In the molecular region, we detected an asymmetric CO clump whose minor axis is closer, with a 24° deviation, to the mean magnetic field orientation than the angle of its major axis. The H i velocity gradients are in general perpendicular to the mean magnetic field orientation except for the region close to the CO clump, where they tend to become parallel. This phenomenon is likely related to gas undergoing gravitational infall. The magnetic field morphology of the target cloud is parallel to the H i column density structure of the cloud in the atomic region, while it tends to become perpendicular to the H i structure in the molecular region. On the other hand, the magnetic field morphology seems to form a smaller offset angle with the total column density shape (including both atomic and molecular gas) of this transition cloud. Conclusions. In the target cloud where the H i–H₂ transition takes place, turbulence is trans-Alfvénic, and hence the magnetic field plays an important role in the cloud dynamics. Atomic gas probably accumulates preferentially along the magnetic field lines and creates overdensities where molecular gas can form. The magnetic field morphology is probed better by the total column density shape of the cloud, and not its H i column density shape.