“Cesar Chavez” is a Mexican-American “42,” a quietly inspiring and well-acted tale of a civil-rights icon whose story isn’t nearly as familiar as Jackie Robinson’s. But then, Chavez wasn’t a ballplayer. He was a union organizer. And while Robinson, with some reluctance, had nobility and greatness thrust upon him, Chavez was a humble farm laborer who set out to be an agent of change.

Actor-turned-director Diego Luna has made an emotional movie with simple human dimensions. Chavez wasn’t a dynamic speaker or necessarily that charismatic. He looked and sounded very ordinary, a modest man driven by simple righteousness. So it’s appropriate that Luna’s film stumbles a little with the sweeping moments in this intimate biography passed off as larger-than-life epic.

Chavez’s struggles to unionize exploited farm workers — his long marches, his hunger strike — make for moving moments but rarely achieve grandeur. It’s the commonplace organizational struggles, the Gandhi-like obsession with nonviolence and the stubborn refusal to be bullied by the bigoted, the rich, the armed and the powerful that stand out in “Cesar Chavez.”

Michael Peña (“End of Watch”) has the title role, a farmworker whose family once had land but lost it in the Depression. He has labored in the fields. He knows the backbreaking work of grubbing up onions or cutting grapes. He knows the campesinos who do that work, with few breaks provided by the growers and no toilets.

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The film picks up his story in the early 1960s. He’s already trying to organize the pickers.

His union bosses in Los Angeles (Rosario Dawson plays one) have been trying and failing to make headway by leafleting and the like. Chavez says, “I wanna get my HANDS dirty.” With his wife (America Ferrara) and eight kids, he moves to Delano, Calif. They work in the fields by day and have meetings by night.

Peña, a low-heat actor in most films, uses that to his advantage here. Chavez was famous for holding his temper. Ferrara gets to be the fiery one, playing a willful woman who brushes aside her husband’s patriarchal sexism, vowing she can get herself arrested just as easily as the next organizer.

John Malkovich plays the face of the opposition, a rich grape-grower who is passing his business on to his son.

Like “42,” “Cesar Chavez” lacks the budget to feel truly epic in scope. But Peña, in the title role, finds the simple dignity in a very basic struggle.