Today, the use of natural biodegradable materials in the production processes is more and more adopted by industry to achieve cyclic economy targets and to improve environmental and human health indexes. Active packaging is the latest trend for food preservation. In this work, nanostructures were prepared by incorporation of thyme oil with natural natrium-montmorillonite and organo-montmorillonite with two different techniques, direct impregnation and the green evaporation–adsorption process. Such nanostructures were mixed with poly-L-lactic-acid for the first time via an extrusion molding process to develop a new packaging film. Comparisons of morphological, mechanical, and other basic properties for food packaging were carried out via XRD, FTIR, TG, SEM/EDS, oxygen and water vapor permeation, and antimicrobial and antioxidant activity for the first time. Results showed that poly-L-lactic-acid could be modified with clays and essential oils to produce improved active packaging films. The final product exhibits food odor prevention characteristics and shelf-life extension capabilities, and it could be used for active packaging. The films based on OrgMt clay seems to be more promising, while the thyme oil addition improves their behavior as active packaging. The PLLA/3%TO@OrgMt and PLLA/5%TO@OrgMt films were qualified between the tested samples as the most promising materials for this purpose.