Manganite perovskites host emerging physical properties of strongly-correlated electrons with charge, spin, and lattice degrees of freedom. Using the epitaxial lift-off technique, we report enhancement of saturation magnetization and the ferromagnetic transition temperature of freestanding La2/3Sr1/3MnO3 membrane compared with as-grown film on SrTiO3 substrate involving lateral tensile strain. Structural analysis reveals shrinkage of unit-cell volume by tensile strain relaxation in the freestanding membrane, which causes enhancement of the ferromagnetic interaction. The impact of the microscopic lattice deformation on the ferromagnetism of La2/3Sr1/3MnO3 indicates a high potential of this material for flexible electronics applications with intriguing functionalities in strongly-correlated electron systems.