Interfaces with subtle differences in atomic and electronic structures in perovskite ABO3 heterostructures often yield intriguingly different properties, yet their exact roles remain elusive. Here, we report an integrated study of unusual transport, magnetic, and structural properties of Pr0.67Sr0.33MnO3 film on SrTiO3 substrate. The variations in the out-of-plane lattice constant and BO6 octahedral rotation across the Pr0.67Sr0.33MnO3/SrTiO3 interface strongly depend on the thickness of the Pr0.67Sr0.33MnO3 film. In the 12 nm film, a new interface-sensitive ferromagnetic polaronic insulator (FI') phase is formed during the cubic-to-tetragonal phase transition of SrTiO3, apparently due to the enhanced electron-phonon interaction and atomic disorder in the film. The transport properties of the FI' phase in the 30 nm film are masked because of the reduced interfacial coupling and smaller interface-to-volume ratio. This work demonstrates how thickness-dependent interfacial coupling leads to the formation of a theoretically predicted ferromagnetic-polaronic insulator, as illustrated in a new phase diagram, that is otherwise ferromagnetic metal (FM) in bulk form.