The structural properties of phase-pure epitaxial (Fe1-xCrx)2O3 thin films deposited on α-Al2O3(0 0 0 1) substrates by oxygen-plasma-assisted molecular beam epitaxy are investigated across the composition range using x-ray photoelectron spectroscopy, high-resolution x-ray diffraction, scanning transmission electron microscopy and electron energy loss spectroscopy, and non-Rutherford resonant elastic scattering measurements. The films possess a columnar grain structure with uniform mixing of cations on the nanometer scale. Fe-rich films are relaxed and appear to be slightly oxygen-rich, while Cr-rich films remain partially strained to the Al2O3 substrate and are found to be oxygen deficient. A model is proposed to explain the oxygen stoichiometry results based on the energetics of oxygen defect formation and rate of oxygen diffusion in the corundum lattice, and the dependence on the cation composition. Deliberately introducing residual compressive biaxial strain into (Fe1-xCrx)2O3 thin films (x = 0, 0.41, 0.52) by employing a Cr2O3 buffer layer is shown to narrow the optical bandgap, from 1.80(1) eV for relaxed (Fe0.47Cr0.53)2O3 to 1.77(1) eV for partially strained (Fe0.48Cr0.52)2O3. The relationships which are elucidated between epitaxial film structure and optical properties can be applied to bandgap optimization in the (Fe,Cr)2O3 system.