Functional foods and the nutritional value of products are now very relevant for consumers. Additionally, interest in biodegradable components made from natural products has recently increased. The aim of this study was to determine the effect of different package types (with addition of films made of biopolymers enriched with natural extracts of ginger, cinnamon, and turmeric) on antioxidative properties of conventional, organic, and wild-grown raspberry fruit during frozen storage for 1-, 4-, 8-, and 12-month periods. The content of total polyphenol and anthocyanins, as well as antioxidant activity, were studied. Additionally, structural (FT-IR and UV-Vis), mechanical (tensile strength and elongation), and surface wetting angle tests of used films were studied. In all crop types, polyphenol content increased at 8 and 12 months of frozen storage in packages with an addition of biopolymer films. There was a statistically significant increase in the amount of total polyphenols in the last month of storage in the package with films with added cinnamon extract. In contrast, packages with ginger-enriched films contributed to an increase in polyphenols only in organically grown and wild raspberry fruit at the 4th, 8th, and 12th month and 8th and 12th month, respectively. The addition of films with turmeric extract increased the polyphenol content in the 8th month of frozen storage of organically grown raspberry fruit and in the 12th month of wild-grown raspberry. During frozen storage of wild raspberry fruit, an increase in anthocyanin content was observed in all cases in the 12th month. This result was almost twice as high as in the control sample. The greatest rise in the content of anthocyanins occurred when packages with films with turmeric extract were applied. Tendencies presented by this paper are not clear-cut in cases of antioxidant activity of analysed raspberries. A common feature was that, in general, after 12 months of storage, raspberries from all crops had higher and statistically significant antioxidant values compared to the first month of storage. Studies on the biocomposite films have shown that the structure of chitosan and alginate polymers was partly decomposed after 12 months, and the natural extracts and raspberry crops used had different effects on the mechanical properties of the biocomposites films. Based on the results of research that has been carried out, it can be concluded that it has not been clearly proven whether the addition of polysaccharide films to packages contributes to the increase in bioactive compounds during frozen storage.