A study was conducted on the biodegradation of aromatic–aliphatic copolyester-based agricultural film in soil at 25 °C. The polymer is known to be biodegradable under composting conditions although rather recalcitrant under mesophilic conditions. The material investigated comprised of the copolyester filled with approximately 25% of starch containing biodegradable plasticizers, and its behavior was compared to the corresponding material without the filler. Mineralization followed by CO2 production merely reached the point of about 6% after 100 days of incubation in the pure copolyester film, whereas the value of around 53% was recorded for the filled copolyester film, which exceeded the readily biodegradable starch filler content in the material by more than 20% and could be accounted for biodegradation of the copolyester. It was suggested that the accelerated copolyester biodegradation in the starch-filled material was most likely explained by the increase in the active surface area of the material available for the microbial attack after biodegradation of the filler. The results were supported by changes in molecular weight distributions of the copolyester and observations made by several microscopic techniques. These findings encourage further development of biodegradable agricultural films based on this material.