Vanillic acid represents a potentially interesting bio-based building block for the production of new aliphatic-aromatic polymers, characterized by thermal properties similar to those of the analogous terephthalic polyesters. However, poly(ethylene vanillate) proved to be a very brittle material, probably due to a very high degree of crystallinity, and, then, not suitable for melt processing. Therefore, the synthesis of copolymers, based on vanillic acid and pentadecalactone is considered as a strategy to obtain new polymeric materials with a low degree of crystallinity, tunable properties, and better performances. The synthesis of these fully bio-based random copolymers is successful. The thermal properties have been studied in order to correlate chemical structure and final performances. The polymers proved to be processable and films are obtained, suggesting possible applications of the copolymers in a new sustainable flexible packaging.