Polylactic acid (PLA) is a key biopolymer with potential uses in numerous sectors, since it is biocompatible and both biobased and biodegradable. However, brittleness limits its industrial applications where plastic deformation at high impact rates or high elongation is required, for instance, flexible food packaging. In order to overcome this drawback and potentially expand the PLA market, we developed flexible PLA materials plasticized with renewable and biodegradable epoxidized soybean oil methyl ester reaching elongations at break of almost 800%. The use of amorphous PLA in combination with the lubricating effect of the plasticizer allowed the more sustainable extrusion at a low temperature of 140 °C, preventing the degradation of PLA and at the same time saving energy. Moreover, plasticized films produced, upon handling, significantly less acoustic noise than pure PLA, which is of great importance for food packaging applications. Morphology, thermomechanical and barrier properties, and migration levels were evaluated as a function of plasticizer content.