Ferroic materials enable a multitude of emerging applications, and optimum functional properties are achieved when ferromagnetic and ferroelectric properties are coupled to a first-order ferroelastic transition. In bulk materials, this first-order transition involves an invariant habit plane, connecting coexisting phases: austenite and martensite. Theory predicts that this plane should converge to a line in thin films, but experimental evidence is missing. Here, the martensitic and magnetic microstructure of a freestanding epitaxial magnetic shape memory film is analyzed. It is shown that the martensite microstructure is determined by an invariant line constraint using lattice parameters of both phases as the only input. This line constraint explains most of the observable features, which differ fundamentally from bulk and constrained films. Furthermore, this finite-size effect creates a remarkable checkerboard magnetic domain pattern through multiferroic coupling. The findings highlight the decisive role of finite-size effects in multiferroics.