Lowering stacking fault energy (SFE) of face-centered cubic (fcc, e.g., Cu) metals by adding alloying elements (e.g., Al) is an effective way to create nanotwins (NTs). In this work, nanostructured Cu thin films with different Al additions (0, 1, 5, and 10 at.%) were prepared by magnetron sputtering deposition on silicon and polymer substrate, respectively, to investigate the effect of lowering SFE on microstructural features and mechanical properties. The Al addition can effectively reduce the SFE of Cu thin films, which in turn promotes the formation of NTs and facilitate the growth of (111) texture but suppresses (100) texture of Cu-Al thin films. Increasing the Al addition to 10 %, the crossed NTs network emerges in the nanostructured Cu-Al thin films. The combined effect of texture and NTs on hardness and ductility was demonstrated, and an optimal hardness/ductility (6.2 GPa/6.3 %) combination was achieved in the Cu-5.0 at.% Al film. Our findings provide deep insight into tailoring the mechanical properties of Cu nanostructures by Al alloying.