Among the many inspired, even wondrous choices made by Ethan Hawke in “The Last Movie Stars” is opening with a clip from “Mr. and Mrs. Bridge.” Adapted from two novels by Evan S. Connell, the 1990 Merchant-Ivory production starred Paul Newman and Joanne Woodward in one of the 16 films the couple made together, and sets them up the same way Mr. Hawke’s documentary series frames them over its six episodes: Newman, even at age 65, seizes the screen, as he had for most of his career. But Ms. Woodward is the subtler artist, delivering a performance of such delicacy that Oscar watchers were probably shocked that she received a Best Actress nomination at all. (And then lost, predictably, to Kathy Bates for “Misery,” thus setting the universe back on its axis.)

The title of the series, originally planned for the defunct CNN+, comes from a quote about the couple by Gore Vidal: “They presided over the end of the movies as the universal art form”—cinema having been overtaken by TV—“so I think people will think of them as the last movie stars.” The soundness of such a statement hinges on one’s definition of stardom, but Mr. Hawke’s premise is that the Newman-Woodward partnership, off-screen and on, survived—with grace—the demise of a Hollywood system that had existed since the ’20s, and on which they themselves had, professionally speaking, grown up.