Nanocomposite biopolymer materials containing colorimetric pH-responsive indicators were prepared from gelatin and chitosan nanofibers. Plant-based extracts from barberry and saffron, which both contained anthocyanins, were used as pH indicators. Incorporation of the anthocyanins into the biopolymer films increased their mechanical, water-barrier, and light-screening properties. Infrared spectroscopy and scanning electron microscopy analysis indicated that a uniform biopolymer matrix was formed, with the anthocyanins distributed evenly throughout them. The anthocyanins in the composite films changed color in response to alterations in pH or ammonia gas levels, which was used to monitor changes in the freshness of packaged fish during storage. The anthocyanins also exhibited antioxidant and antimicrobial activity, which meant that they could also be used to slow down the degradation of the fish. Thus, natural anthocyanins could be used as both freshness indicators and preservatives in biopolymer-based nanocomposite packaging materials. These novel materials may therefore be useful alternatives to synthetic plastics for some food packaging applications, thereby improving the environmental friendliness and sustainability of the food supply.