Electrospun scaffolds made of nano- and micro-fibrous non-woven mats from biodegradable polymers have been intensely investigated in recent years. In this field, polymer-based materials are broadly used for biomedical applications since they can be managed in high scale, easily shaped, and chemically changed to tailor their specific biologic properties. Nonetheless polymeric materials can be reinforced with inorganic materials to produce a next-generation composite with improved properties. Herein, the role of graphene nanoplatelets (GNPs) on electrospun poly-l-lactide-co-poly-ε-caprolactone (PLA–PCL, 70:30 molar ratio) fibers was investigated. Microfibers of neat PLA–PCL and with different amounts of GNPs were produced by electrospinning and they were characterized for their physicochemical and biologic properties. Results showed that GNPs concentration notably affected the fibers morphology and diameters distribution, influenced PLA–PCL chain mobility in the crystallization process and tuned the mechanical and thermal properties of the electrospun matrices. GNPs were also liable of slowing down copolymer degradation rate in simulated physiological environment. However, no toxic impurities and degradation products were pointed out up to 60 d incubation. Furthermore, preliminary biologic tests proved the ability of the matrices to enhance fibroblast cells attachment and proliferation probably due to their unique 3D-interconnected structure.