The orientation relationships (ORs) of copper crystals on a sapphire substrate equilibrated at 1253 K are presented. They barely depend on the procedures used in sample preparation, i.e. dewetting of a copper film in the liquid state or in the solid state. The most frequent OR found is Cu(111) || Al2O3 and Cu within few degrees from Al2O3[0001]. A secondary, lower frequency OR is also observed: Cu(001) || Al2O3 with Cu within a few degrees from either Al2O3 or Al2O3[0001]. These ORs do not follow the Fecht and Gleiter model which proposes that dense directions of the metal should align with dense directions of the oxide. On annealing, even at a temperature about half of the melting point of sapphire, fast diffusion of sapphire at the copper/sapphire interface is observed: the copper particles tend to achieve their interfacial equilibrium shapes by sinking into the substrate, and sapphire ridges form at the triple line. Finally, it is shown that the Cu(111) || Al2O3 interface remains flat at the atomic scale, and is therefore part of the copper/sapphire equilibrium interfacial shape.