Biodegradable packaging plastics combining good mechanical properties and low gas permeability is required to avoid environmental and food safety concerns. This study explores the impact of montmorillonite (MMT) and halloysite nanotubes (HNT), on the mechanical, optical, and oxygen permeability of blown film poly (butylene adipate‐co‐terephthalate) (PBAT) composites. The morphology of the films was evaluated by x‐ray diffraction (XRD), differential scanning calorimetry and scanning electron microscopy. Good distribution/dispersion of clays is found in the PBAT‐MMT films. Besides, there is an increase in the crystallinity of PBAT due to the nucleating effect of HNT. Improvement in the tensile strength and elongation at break in the machine direction is obtained up to a clay content of 1.5 vol%. The incorporation of 1.5 vol% of MMT and 1 vol% of HNT leads to a reduction in the oxygen permeability of the PBAT film by 29% and 38% respectively. Furthermore, the films remain transparent regardless of clay content. Finally, the feasibility of the films for food storage is tested in grapes, obtaining extended shelf life. The favorable mechanical, barrier and optical properties of the biodegradable films, along with the scalable production process, make them attractive for application in the storage and preservation of food products.