Measurements of electric- and magnetic-field-induced changes in electrical conduction indicate the coexistence of charge-ordered and ferromagnetically ordered regions in the Sr-substituted Pr0.7Ca0.3MnO3 epitaxial films. Percolative, metal-like channels open up in this topologically inhomogeneous medium on the application of these fields, and a technologically promising orders-of-magnitude drop in resistance ensues. Measurements of current-voltage characteristics and the temperature dependence of resistivity show hysteretic and history effects, which are intimately linked to the relative stability of the two phases.