The ambitions of “George & Tammy,” a new limited series about two of the entertainment industry’s true individuals, seem to be to duplicate another show’s success.

In its structure and its concerns, the series feels as though it owes a debt to “Fosse/Verdon,” FX’s excellent 2019 series about two creative and romantic partners trying to make love and art, together and apart. “George & Tammy,” like “Fosse/Verdon,” draws on the recollections of its subjects’ daughter; this new series assays the life and work of country singers George Jones and Tammy Wynette at various key moments. But while it nails the fundamental music-biography beats, it can’t find the spark or soul that characterizes the best country songs.

Michael Shannon and Jessica Chastain play the stars here; the series begins with George as an established name, and Tammy seeking the break that will bring her out of obscurity. After a chance meeting, they’re drawn to one another both as artists and as lovers, and Shannon and Chastain leverage their charisma to make the potency of their bond clear from the first. The musical side of things is a harder sell: Shannon acquits himself well, but Chastain’s voice is not one, perhaps, that is best-suited to the simultaneous delicacy and strength of Wynette’s hits. (There’s more than a little of her other Tammy, the Oscar-winning role of Tammy Faye Bakker, in the mix here.)

Country music is all about storytelling, and Jones and Wynette lived the kind of lives that you could write a truly sad song about, from the euphoric highs of lust and career success to the painful lows of addiction and health struggles and marital strife. That makes it all the more confounding that there’s no transformative or transcendent aspect to this show’s run-through of the facts of its central couple’s life. John Hillcoat, who directs, moves the story at a somewhat languid pace: Time and again, an event happens, and we sit with the latest triumph or setback for a long moment before moving on to the next thing. George and Tammy are people to whom a great deal happened. But they lack the texture of excellent characters.

The series, the debut episode of which is to air on Showtime and the Paramount Network, makes for a red-state double feature with “Yellowstone,” which will lead into it on Paramount. And it seems to be drawing on the name recognition of subjects and stars both. The fundamental thing that turns mediocre-or-worse projects like “Bohemian Rhapsody” into smashes is in evidence here: If you want to spend six hours watching two movie stars singing great songs, you are in luck. (No country aficionado myself, I found myself seeking out Tammy Wynette’s music between episodes.) But what’s lacking here, the thing “Fosse/Verdon” drew out of Sam Rockwell and Michelle Williams as they crafted a similar-on-the-surface dance of love and hate, is a sense of why the story being told matters, to the wider world or even to the people on screen.

“George & Tammy” will premiere simultaneously on Showtime and the Paramount Network on Sunday, December 4 at 9 p.m. ET/PT. The remainder of the season will be available exclusively on Showtime, with new episodes streaming Fridays and airing Sundays at 9 p.m.