Biodegradable polymeric films have great potential as alternatives to synthetic polymeric films to reduce environmental pollution. Plasticizing agents and nanofillers can improve the mechanical properties of polymer-based composites, resulting in materials with better flexibility and extensibility. Starch, a natural polymer, can be produced at low cost and on a large scale from abundant and inexpensive agricultural resources like potatoes. The aim of the present work was to fabricate mechanically strong and thermally stable potato starch films reinforced with different types of plasticizers and nanoclays at different concentrations. Different types of plasticizers such as water, glycerin, ethylene glycol, sorbitol, and formamide and three types of clays such as montmorillonite, hectorite, and kaolinite at various concentrations were used to prepare potato starch-based nanocomposite films. The films were prepared using a very simple solution casting process. The mechanical properties and thermal stabilities of nanocomposite films significantly improved using montmorillonite, hectorite, and kaolinite clays. The water uptake percentage of the fabricated films decreased with addition of plasticizers and further decreased with addition of different types of clays. The structural and morphological changes of the fabricated films in the presence of plasticizers and nanoclays were correlated in detail with their mechanical properties, crystallinity, biodegradability, thermal stability, and water absorption capacities.