Wounds disrupt the proper function of the skin, and the use of biocompatible films ensures the right conditions for wound healing, prevents microbial infection and thus leads to skin regeneration. Chitosan (CS) is a natural polymer with healing properties, and polyvinyl alcohol (PVA) is a synthetic, biocompatible polymer which increases mechanical properties. In this study, the films used are based on biocompatible hydrogels that are produced via the action of hyaluronic acid (HA) as a natural cross-linker and the interactions between the polymeric chains of CS, PVA and HA. The incorporation of curcumin (Cur) (a natural antimicrobial agent) ensures the protection of the wound against pathogenic microbes. The combination of these materials offers a novel approach to enhancing the water sorption, stability and functionality of wound-healing films. Thus, two groups of films were prepared—CS/PVA@HA and CS/PVA@HA/Cur—with varying concentrations of HA (0.5, 1, 2, 3% w/w) and a fixed concentration of PVA (1% w/v), CS (2% w/v) and Cur (0.1% w/w). The characteristic peaks of the films in FTIR appear to be slightly shifted, which confirms the cross-linking between the chains, while XRD is included. Moreover, swelling and stability assays proved that CS/PVA@HA and CS/PVA@HA/Cur containing 2% w/w HA exhibited optimal behavior under conditions of swelling and stability at pH 5.6 and 7.4, respectively. The results of the experiments confirmed the successful synthesis of the films via our physical cross-linking method. It was found that the incorporation of HA in the CS/PVA polymer network increased the water sorption and swelling behavior of the prepared materials. Therefore, the biocompatibility and the cell growth capacity of the films were also confirmed. Thus, they have potential as wound dressings, with easy formation and improved bio-evaluations for wound-dressing applications.