The dancers streamed across the stage of a historic Paris theater, leaping and turning, the women lifted high into the air and whirled aloft, before aligning to bow on the final chords of the music. “Bravo! Bravo!” cried the enthusiastically applauding audience.

Then Amy Sherman-Palladino, sporting a white baseball cap, walked onstage with a Steadicam operator, consulted the choreographer Marguerite Derricks, and clapped her hands sharply. “Let’s go!” she called. Moments later, the cameraman was running frantically amid the dancers as Sherman-Palladino peered at a monitor, watching the way their movement was captured from inside the groupings.

“That was great, you guys were fabulous,” she called out at the end. She turned to the audience “What do you think?” Much applause. The cameraman took a little bow.

It was last May at the Théâtre du Châtelet, where Sherman-Palladino; her husband and creative partner, Daniel Palladino; and their team were filming “Étoile,” a new Amazon Prime Video series debuting on Thursday.

The show (the title means “star” in French) tells the story of two major ballet companies — the Ballet National (a thinly veiled Paris Opera Ballet), and the New York-based Metropolitan Ballet Theater (a mash-up of American Ballet Theater and New York City Ballet) — collaborating on an exchange of artists in order to boost sales and drum up publicity.