Bone tissue engineering is an emerging field, representing one of the most exciting challenges for scientists and clinicians. The possibility of combining mesenchymal stem cells and scaffolds to create engineered tissues has brought attention to a large variety of biomaterials in combination with osteoprogenitor cells able to promote and regenerate bone tissue. Human adipose tissue is officially recognized as an easily accessible source of mesenchymal stem cells (AMSCs), a significant factor for use in tissue regenerative medicine. In this study, we analyze the behavior of a clonal finite cell line derived from human adipose tissue seeded on poly(ε-caprolactone) (PCL) film, prepared by solvent casting. PCL polymer is chosen for its good biocompatibility, biodegradability, and mechanical properties. We observe that AMSCs are able to adhere to the biomaterial and remain viable for the entire experimental period. Moreover, we show that the proliferation process and osteogenic activity of AMSCs are maintained on the biofilm, demonstrating that the selected biomaterial ensures cell colonization and the development of an extracellular mineralized matrix. The results of this study highlight that AMSCs and PCL film can be used as a suitable model to support regeneration of new bone for future tissue engineering strategies.