The Fugitive (1963)

While hoping freight trains, Kimble meets a young woman named Carol Hollister with her baby whom she is traveling to meet her husband. But Kimble doesn't know that Carol is a mentally disturbed young woman whose newborn baby died a year earlier and she has abducted another baby. Soon, Carol becomes so far gone that she mistakes Kimble as her late husband. Kimble must find a way to get the baby away from Carol and return it to it's rightfull parents while avoiding the police looking for her.