We performed atomic-scale ab initio calculations to investigate the stacking fault (SF) properties of the metastable ζ-Zr2H zirconium hydride. The effect of H near the SF was found to entail the existence of negative SF energies, showing that the ζ compound is probably unstable with respect to shearing in the basal plane. The effect of temperature on SFs was investigated by means of free energy calculations in the quasiharmonic approximation. This evidenced unexpectedly large temperature effects, confirming the main conclusions drawn at 0 K, in particular the ζ mechanical instability. The complex behaviour of H atoms during the shear process suggested ζ-hcp  →  Zr2H-fcc as a plausible shear path leading to an fcc compound with same composition as ζ. Finally, as shown by an analysis based on microelasticity, this Zr2H-fcc intermediate compound may be relevant for better interpreting the currently intricate issue of hydride habit planes in zirconium.