Despite significant interest in developing extracellular matrix (ECM)-inspired biomaterials to recreate native cell-instructive microenvironments, the major challenge in the biomaterial field is to recapitulate the complex structural and biophysical features of native ECM. These biophysical features include multiscale hierarchy, electrical conductivity, optimum wettability, and mechanical properties. These features are critical to the design of cell-instructive biomaterials for bioengineering applications such as skeletal muscle tissue engineering. In this study, we used a custom-designed film fabrication assembly, which consists of a microfluidic chamber to allow electrostatic charge-based self-assembly of oppositely charged polymer solutions forming a hydrogel fiber and eventually, a nanocomposite fibrous hydrogel film. The film recapitulates unidirectional hierarchical fibrous structure along with the conductive properties to guide initial alignment and myotube formation from cultured myoblasts. We combined high conductivity, and charge carrier mobility of graphene with biocompatibility of polysaccharides to develop graphene-polysaccharide nanocomposite fibrous hydrogel films. The incorporation of graphene in fibrous hydrogel films enhanced their wettability, electrical conductivity, tensile strength, and toughness without significantly altering their elastic properties (Young's modulus). In a proof-of-concept study, the mouse myoblast cells (C2C12) seeded on these nanocomposite fibrous hydrogel films showed improved spreading and enhanced myogenesis as evident by the formation of multinucleated myotubes, an early indicator of myogenesis. Overall, graphene-polysaccharide nanocomposite fibrous hydrogel films provide a potential biomaterial to promote skeletal muscle tissue regeneration.