Nanocomposite films that were based on furcellaran (FUR) and nanofillers (carbon quantum dots (CQDs), maghemite nanoparticles (MAN), and graphene oxide (GO)) were obtained by the casting method. The microstructure, as well as the structural, physical, mechanical, antimicrobial, and antioxidant properties of the films was investigated. The incorporation of MAN and GO remarkably increased the tensile strength of furcellaran films. However, the water content, solubility, and elongation at break were significantly reduced by the addition of the nanofillers. Moreover, furcellaran films containing the nanofillers exhibited potent free radical scavenging ability. FUR films with CQDs showed an inhibitory effect on the growth of Staphylococcus aureus and Escherichia coli. The nanocomposite films were used to cover transparent glass containers to study the potential UV-blocking properties in an oil oxidation test and compare with tinted glass. The samples were irradiated for 30 min. with UV-B and then analyzed for oxidation markers (peroxide value, free fatty acids, malondialdehyde content, and degradation of carotenoids). The test showed that covering the transparent glass with MAN films was as effective in inhibiting the oxidation as the use of tinted glass, while the GO and CQDs films did not inhibit oxidation. It can be concluded that the active nanocomposite films can be used as a desirable material for food packaging.