In the last years, the exponential growth in the demand of petroleum-based plastic materials, besides the extreme exploitation of nonrenewable resources, lead to the mismanagement of their disposal and to serious ecological issues related to their dispersion in the environment. Among the possible practical solutions, the design of biobased and biodegradable polymers represents one of the most innovative challenges. In such a context, the eco-design of an aromatic-aliphatic multiblock copolymer based on poly(lactic acid) and containing 2,5-furandicarboxylic acid was carried out with the aim of improving the properties of poly(l-lactic acid) for sustainable packaging applications. The synthetic method followed a novel top-down approach, starting from industrial high-molecular-weight poly(l-lactic acid) (PLLA), which was reacted with 1,5-pentanediol to get hydroxyl-terminated PLLA and then chain-extended with hydroxyl-terminated poly(pentamethylene furanoate) (PPeF-OH). The final copolymer, called P(LLA50PeF50)-CE, was subjected to molecular, structural, and thermal characterization. Tensile and gas permeability tests were also carried out. According to the results obtained, PLLA thermal stability was improved, being the range of processing temperatures widened, and its stiffness and brittleness were decreased, making the new material suitable for the realization of films for flexible packaging. The oxygen permeability of PLLA was decreased by 40% and a similar improvement was measured also for carbon dioxide. P(LLA50PeF50)-CE was found to be completely biodegraded within 60 days of composting treatment. In terms of mechanism, the blocks of PPeF and PLLA were demonstrated to undergo surface erosion and bulk hydrolysis, respectively. In terms of kinetics, PPeF blocks degraded slower than PLLA ones.