Polylactide (PLA) is among the most commonly used polymers for biomedical applications thanks to its biodegradability and cytocompatibility. However, its inherent stiffness and brittleness are clearly inappropriate for the regeneration of soft tissues (e.g., neural tissue), which demands biomaterials with soft and elastomeric behavior capable of resembling the mechanical properties of the native tissue. In this work, both L- and D,L-lactide were copolymerized with ethylene brassylate, a macrolactone that represents a promising alternative to previously studied comonomers (e.g., caprolactone) due to its natural origin. The resulting copolymers showed an elastomeric behavior characterized by relatively low Young’s modulus, high elongation at break and high strain recovery capacity. The thermoplastic nature of the resulting copolymers allows the incorporation of nanofillers (i.e., carbon nanotubes) that further enable the modulation of their mechanical properties. Additionally, nanostructured scaffolds were easily fabricated through a thermo-pressing process with the aid of a commercially available silicon stamp, providing geometrical cues for the adhesion and elongation of cells representative of the nervous system (i.e., astrocytes). Accordingly, the lactide and ethylene brassylate-based copolymers synthesized herein represent an interesting formulation for the development of polymeric scaffolds intended to be used in the regeneration of soft tissues, thanks to their adjustable mechanical properties, thermoplastic nature and observed cytocompatibility.