Pulsed-laser ablation of zinc and iron-based oxide targets leads to the growth on c-cut sapphire substrates of nanocomposite films constituted by randomly distributed wurtzite (Fe:ZnO) and spinel (Zn:Fe3O4) phases. By the complementary use of Rutherford backscattering spectrometry, X-ray diffraction and transmission electron microscopy, the nature and composition of the phases, their structure and microstructure were investigated. Both phases are textured, (0001) and (111) for the wurtzite and spinel, respectively. The epitaxial relationships with the sapphire substrate were determined: the wurtzite crystallites present the classical 30 degrees rotation of the hexagon of their (0001) plane with respect to the hexagon of the (0001) Al2O3 plane. The spinel crystallites show two in-plane orientations, one corresponding to the 30 degrees rotation of the hexagon of their (111) planes, the other one being at 0 degrees. These two in-plane epitaxial orientations were observed for spinel crystallites directly grown on (0001) Al2O3 as well as for spinel crystallites inside the nanocomposite films. They are shown to be related to differences in the Zn concentration inside the spinel. A high Zn concentration (> 33%) leads to the hexagon on hexagon 0 degrees epitaxy while a lower concentration leads to the 30 degrees rotation. This lead us to conclude in differences in the epitaxy of the inverse spinel (low Zn concentration in the crystallite) and of the normal spinel (high Zn concentration).