Rapeseed protein-based nanocomposite films were developed through a compression molding process, incorporating cellulose nanocrystals (CNC), surface-modified montmorillonite (MMT), and hydroxyapatite (HA) as nanofillers. The primary aim of this study was to enhance the properties of the bioplastic films, specifically focusing on potential applications in food packaging. The results demonstrated that bioplastic films containing 3% nanofillers exhibit superior properties compared to the control film. The improved characteristics of nanocomposite films based on rapeseed proteins are attributed to the synergistic interactions between the nanofillers and the protein matrix. Notably, CNC displayed optimal mechanical properties, with a tensile strength of 7.2 ± 2 MPa and a percent elongation of 128 ± 4%. In contrast, HA had a less pronounced effect, yielding values of 5.6 ± 1.3 MPa and 149 ± 9%, respectively. Similarly, MMT had a comparatively weaker impact, resulting in values of 4.4 ± 1.2 MPa and 44 ± 5%. The influence of storage at 25 °C on the stability of the films was also examined. Prolonged storage under uncontrolled conditions accelerated the aging process of the films primarily due to plasticizer migration and moisture loss. These changes not only affected the films' characteristics but also induced changes in their secondary structure and arrangement. Conversely, the incorporation of nanofillers enhanced film stability, mitigating plasticizer migration and thereby slowing the aging process. Overall, the findings suggest that compression-molded rapeseed protein-cellulose nanocrystal nanocomposite (RP-CNC) is well suited for packaging applications, maintaining stability for up to 4 weeks of storage under room-temperature conditions.