We study structural phase transitions among modulated phases of liquid-crystal films. As a function of an applied electric field, we find that both square-lattice and hexagonal modulated phases are possible. The latter are similar to hexagonal phases predicted for smectic-C* films. In contrast with reconstructive transitions, however, we predict that the square-lattice modulated phase can undergo a continuous evolution to the hexagonal phase. Intermediate between these two phases is a phase of lower symmetry.