Nanocomposite materials are increasingly commonly used to ensure food safety and quality. Thanks to their unique properties, stemming from the presence of nanoparticles, they are used to develop advanced sensors and biosensors, e.g., for various harmful substances, heavy metals, microorganism growth, and environmental changes in food products. The aim of this study is to produce novel films based on natural resources—potato starch and chitosan—incorporating generated quantum dots of zinc sulfide and cadmium sulfide. The biocomposites were subjected to the following assays: FTIR spectroscopy, UV-VIS spectroscopy, photoluminescence spectroscopy, and SEM/TEM spectroscopy. Their mechanical properties were also analyzed, a colorimetric analysis was performed, and the water content, solubility, and water absorption capacity were determined. A storage test was also performed, using poultry meat covered with the produced films, to assess the microbiological quality. The results confirmed the presence of the quantum dots in the starch–chitosan matrix. The unique optical properties of the films were also demonstrated. It was shown that the composites with nanoparticles limited the growth of selected microorganisms in poultry meat. The food storage time was found to have an impact on the fluorescent properties of the composites. The results point to the possibility of using the produced films as active and smart packaging.