Preparation of biodegradable packaging materials and valorisation of food industry residues to achieve “zero waste” goals is still a major challenge. Herein, biopolymer-based (carboxymethyl cellulose—CMC) bioactive films were prepared by the addition, alone or in combination, of carvacrol and fungal melanin isolated from champignon mushroom (Agaricus bisporus) agro-industrial residues. The mechanical, optical, thermal, water vapour, and UV-Vis barrier properties were studied. Fourier-transform infrared (FT-IR) spectroscopy studies were carried out to analyse the chemical composition of the resulting films. Antibacterial, antifungal, and antioxidant activities were also determined. Both CMC/melanin and CMC/melanin/carvacrol films showed some antimicrobial activity against Escherichia coli, Staphylococcus aureus, and Candida albicans. The addition of melanin increased the UV-blocking, mechanical, water vapour barrier, and antioxidant properties without substantially reducing the transparency of the films. The addition of carvacrol caused loss of transparency, however, composite CMC/melanin/carvacrol films showed excellent antioxidant activity and enhanced mechanical strength. The developed bioactive biopolymer films have a good potential to be green bioactive alternatives to plastic films in food packaging applications.