Blends of poly(lactic acid) (PLA)/poly(butylene adipate‐co‐terephthalate) grafted with glycidyl methacrylate (PBAT‐g‐GMA) were developed to produce flat and flexible biofilms through extrusion. The PLA/PBAT‐g‐GMA (90%/10%, 80%/20%, 70%/30%, and 60%/40% by mass) blends were processed in the internal mixer, injection molded, and manufactured into flat films. The optimal composition to produce flexible biofilms was PLA/PBAT‐g‐GMA (60/40%), as it demonstrated a decrease in elastic modulus of 53.2% and a significant gain in elongation at a break of 4923% about pure PLA. The incorporation of 40% PBAT‐g‐GMA in PLA increased the torque (Z) by 208%, while the melt flow index (MFI) decreased by 51.57%, compared to PLA. Additionally, the degradation rate (Rz) and molar mass loss (Rm) during processing were minimized, indicating that 40% PBAT‐g‐GMA enhanced stability of the PLA matrix. Fourier transform infrared spectroscopy indicated interactions between the GMA of PBAT‐g‐GMA and PLA, justifying the increase in viscosity and elongation at break. The PLA/PBAT‐g‐GMA (60/40%) composition showed a transmittance in the range of 20%–48% (400–800 nm) and an oxygen gas permeability of 1.56 × 10−5 cm3 STP/cm−2 h bar, indicating its potential for applications in packaging with optical barrier properties. Scanning electron microscopy (SEM) revealed ligaments in the interfacial region between PLA and PBAT‐g‐GMA, confirming the good performance in elongation at break. The results presented are essential for the plastics processing sector, aiming to develop eco‐friendly packaging.