We report a detailed study of the growth and structure of thin films of copper hexadecafluorophthalocyanine (F16CuPc) on sapphire. These films show very good out of plane order and have X-ray rocking widths of around 0.02degrees. If prepared under suitable conditions of A-plane sapphire substrates, the molecules align without significant azimuthal dispersion. Growth on MgO (001) and oxidized silicon wafers resulted in a comparable out-of-plane structure, but showed no azimuthal order. We find that he azimuthal alignment on sapphire is induced by the step edges along the c-axis of the sapphire, which serve as templates for the growth. For growth at different substrate temperatures, we find a monotonic change of the molecular out-of-plane tilt angle, as obtained from Raman scattering, which is accompanied by a change of the out-of-plane lattice parameter.