A new active composite film intended for bread packaging is described here. The active film has the aim of prolonging bread’s shelf life while avoiding the use of nanoparticles that, with very few exceptions, are a type of material not allowed by regulatory agencies like EFSA (European Food Safety Agency) and FDA (US Food and Drug Administration) in food contact materials. Moreover, the increasing consumer demand for natural and wholesome products, possibly “clean label”, and packaged in natural, non-petroleum-based materials has been taken into consideration. Accordingly, precursor materials from renewable sources were used to prepare the active film: pectin from citrus peel (PEC) and carboxymethyl cellulose (CMC) were used as the matrix, with oleic acid (OA) as plasticizer. Moreover, the bread preservative calcium propionate (CaP) was used as the crosslinker, and also zeolite microparticles loaded with silver ions (AgZ) were added to the films as an additional antimold agent. This strategy allows us to avoid the addition to bread of the now commonly used preservatives ethanol and calcium propionate, moving the latter to the packaging. Permeance measurements revealed excellent barrier properties against O₂ and CO₂, while the typical high water vapor permeance of polysaccharide films was mitigated by the non-hydrophilic OA plasticizer. Moreover, the quantities of Ag⁺ and CaP released in bread are low and below the limits imposed by regulatory agencies. The antimold activity of the films is excellent, with Aspergillus niger, Penicillium janthinellum, and wild-type Penicillim molds reduction on bread in the 99.20–99.95% range for the films containing only CaP and in the 99.97–99.998% range for the films containing both CaP and AgZ. Finally, the rheological properties of the film-forming solutions were investigated, demonstrating their potential application as coatings on natural packaging materials for bread, such as paper.