Poly-ε-caprolactone (PCL)-based nanocomposite scaffolds with different concentrations of carbon nanofillers (carbon nanofibers (CNFs), nanographite, and exfoliated graphite) have been studied to investigate the effect of electrical conductivity and biomolecule supplementation for enhanced human meniscal cell attachment, growth, and proliferation. The incorporation of carbon nanofillers was found to improve the mechanical and electrical properties. CNF-based nanocomposite scaffolds showed the highest electrical conductivity with significant improvements in mechanical properties (more than 50% tensile strength increase than PCL with 10% (w/w) CNF). All nanocomposite scaffolds were subjected to cytotoxicity studies using primary meniscus cells. The nanocomposite scaffolds showing higher cell viability were selected and tested for meniscal cell attachment and proliferation assays such as total deoxyribonucleic acid content, extracellular matrix secretion, nuclear staining, and cell attachment studies using a scanning electron microscope. When an optimized combination of biomolecules is supplemented in the cell culture medium, a synergistic effect of the electrical conductivity and biomolecule combination is observed, especially in the case of highly conducting CNF (7.5% and 10% (w/w))-based nanocomposite scaffolds. Our findings suggest that electrically conductive scaffolds with optimized biomolecules in cell culture medium can potentially be used for successful human meniscal tissue engineering applications.