"He is doing all he can to get Natalie to forgive him and keep their family together," a source tells PEOPLE
Their marriage is the subject of a new article in the French outlet Voici, which claims Millepied had an extramarital affair. A source tells PEOPLE, "It was short-lived and it is over."
Portman, 41, and director/choreographer Millepied, 45, who met on set of the 2010 movie Black Swan, remain together despite his "enormous mistake," a source close to the couple tells PEOPLE.
"He knows he made an enormous mistake and he is doing all he can to get Natalie to forgive him and keep their family together," says the source. "Natalie is incredibly private and has no intention of playing this out in the media. Her biggest priority is protecting her children and their privacy."
Reps for Portman and Millepied had no immediate comment.
The couple wed on Aug. 4, 2012. Portman celebrated their 10-year wedding anniversary in August 2022 with an Instagram tribute, writing at the time alongside a photo of them together, "Ten years today @benjaminmillepied, and it keeps getting better…"
Portman supported Millepied on the red carpet in September for the Toronto International Film Festival premiere of Carmen, which he directed. The movie debuted in theaters in April, though he attended the premiere that month solo.
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Then, in May, Portman walked red carpets solo: for the Los Angeles premiere of her HBO docuseries Angel City, and at the Cannes Film Festival, where she rolled out her movie with Julianne Moore, May December.
Portman previously recalled meeting Millepied while making Black Swan back in 2009, where Millepied was the film's choreographer as she learned the ballet sequences.
"I met my husband on it, so I think I was in, like, dreamland," Portman said during a SiriusXM Town Hall interview in 2018. "... He was teaching me to dance. You know, one of those romantic [stories] … It was definitely exciting and fun. It was beautiful. I don't know about instant. It was like I really got to know him and that was when it seemed like, 'Oh this is the person.' "
Portman and Millepied collaborated again on her 2018 film Vox Lux, in which she played a troubled pop star. The Oscar winner told PEOPLE at the time why she enjoyed working with her husband on the project.
"It was really fun because I think he knows me so well, and what my strengths and weaknesses are in dancing, that he was really able to create choreography very seamlessly and quickly because we had very little time," she said. "So it was very convenient that he knew me so well and that he's as talented as he is."
Continued Portman, "It was fun to get to watch him create because I don't often watch him in the studio. Just to see the ease and the expertise that he has, and of course with different kinds of dance too, was really, really stunning."
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