The use of essential oil components as natural antifungal preservatives in the active packaging of bread is an innovative approach that leverages the antimicrobial properties of these compounds to extend the shelf life of bread and ensure its safety. The aim of the present work was the thorough investigation of the antioxidant properties and antifungal activity of low-density polyethylene (LDPE or PE) nanocomposite films with organically modified montmorillonite (O) loaded with carvacrol (C) or thymol (T) as a function of time, starting from 2 months and concluding at 12 months. The films PE_OC and PE_OT were prepared through the evaporation/adsorption method, a green methodology developed by our group compatible with food packaging. For a comprehensive analysis of the synthesized films' oxygen permeability (OTR), measurements were employed, indicating that the incorporation of clay-bioactive nanocarriers into LDPE films reduced their oxygen permeability. A thorough analysis in terms of the antioxidant activity of the films was assessed at various intervals (2, 3, 6, and 12 months), showing high antioxidant activity for films PE_OC10 and PE_OT10 (polyethylene with 10% wt. organically modified montmorillonite loaded with carvacrol or thymol), even at 12 months. Based on the overall analysis, the PE_OC10 film was identified as the most effective option in the antifungal evaluation conducted using white bread, demonstrating substantial inhibition of fungal growth for up to six months.