Sustainable hydrocolloid-based films containing natural antioxidants, caffeic and p-coumaric acids at different concentrations of 0.5%, 1%, 5%, and 10% w/w of polymers, were designed for packing fatty foods. Antioxidant activities and kinetics for all film formulations were assessed using radical scavenging activity (DPPH), reducing power, and iron chelating ability. Release kinetics of the antioxidants from the films into a food simulant (96% ethanol) were analyzed. The intermolecular interactions between antioxidants and polymers chains were assessed by Fourier transform infrared attenuated total reflectance (FTIR-ATR) and related to the film properties. Antioxidant activity of pure compounds (powder), showed that caffeic acid (IC = 4 μg/mL) had higher activity than p-coumaric acid (IC = 33 μg/mL). Films containing caffeic acid exhibited higher antioxidant activity, reducing power, and iron chelating ability than p-coumaric acid films. The antioxidant activity is concentration dependent. However, the percentage of release (PR) in ethanol (96%) is not influenced by the initial concentration. PR is 88% ± 9% and 82% ± 5%, respectively, for caffeic and p-coumaric acids. Determination of the partition ( K) and the apparent diffusion ( D) coefficients allowed better characterization of the release kinetic mechanisms. The partition coefficients of caffeic acid ( K = 454) and p-coumaric acid ( K = 480) are not influenced by the initial concentration. The diffusion coefficients ( D) of caffeic and p-coumaric acids were of same order, but they slightly increased with the antioxidant concentration and probably related to antioxidant activity. FTIR displayed that amide B and amide-III are involved in the interactions occurring between polymer chains and antioxidants. However, interactions are of only low energy and unable to significantly affect the structure of films and consequently the release kinetics.