Argentina’s 1976 military coup d’état, along with the sustained period of violence and forced disappearances that it ushered in, isn’t an obvious historical backdrop for a heartwarming tale of human-animal bonding. But that’s how the timing worked out for Tom Michell, an English teacher stationed at an elite Buenos Aires private school, at the time of the turmoil: With the country in chaos and many of his colleagues in crisis, he was figuring out what to do with the Magellan penguin he had accidentally adopted on a weekend jaunt to Uruguay. His 2016 memoir of that period, “The Penguin Lessons,” was the kind of breezy read that bridges adult and juvenile tastes for animal stories; Peter Cattaneo’s amiable film adaptation matches the book’s feathery whimsy while reaching for a little more political import. Almost inevitably, it’s best when it’s about the bird.

While Michell...