A source tells PEOPLE of the extramarital affair: "It was short-lived and it is over"
The two were photographed at Georges in Paris on Monday. In the photo, Portman, 41, is seen smiling and chatting with Director Todd Haynes.
The outing occurred just days before the French outlet Voici, alleged that the director had an extramarital affair. While reps for Portman and Millepied had no immediate comment, a source told PEOPLE that it "was short-lived and it is over." Together, the couple are parents to son Aleph, 12 this month, and daughter Amalia, 6.
Speaking about the current status of their relationship, a source close to the couple tells PEOPLE that they remain together.
"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," the source said. "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."
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.
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.
The couple first met in 2009 after Portman signed on for a starring role in Black Swan, while Millepied was hired to choreograph the film. She recalled the experience during a SiriusXM Town Hall interview explaining that it was a "dreamland."
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"I met my husband on it, so I think I was in, like, dreamland … We had a whole, like, 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,'" she said.
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