The Italian actress and director Asia Argento was among the first women in the movie business to publicly accuse the producer Harvey Weinstein of sexual assault. She became a leading figure in the #MeToo movement. Her boyfriend, the culinary television star Anthony Bourdain, eagerly joined the fight.

But in the months that followed her revelations about Mr. Weinstein last October, Ms. Argento quietly arranged to pay $380,000 to her own accuser: Jimmy Bennett, a young actor and rock musician who said she had sexually assaulted him in a California hotel room years earlier, when he was only two months past his 17th birthday. She was 37. The age of consent in California is 18.

That claim and the subsequent arrangement for payments are laid out in documents between lawyers for Ms. Argento and Mr. Bennett, a former child actor who once played her son in a movie.

The documents, which were sent to The New York Times through encrypted email by an unidentified party, include a selfie dated May 9, 2013, of the two lying in bed. As part of the agreement, Mr. Bennett, who is now 22, gave the photograph and its copyright to Ms. Argento, now 42. Three people familiar with the case said the documents were authentic.

Mr. Bennett, who lives in Los Angeles, would not agree to be interviewed, said his lawyer, Gordon K. Sattro. “In the coming days,” Mr. Sattro wrote in an email, “Jimmy will continue doing what he has been doing over the past months and years, focusing on his music.”

“We hope nothing like this ever happens to you again,” Ms. Goldberg wrote. “You are a powerful and inspiring creator and it is a miserable condition of life that you live among shitty individuals who’ve preyed on both your strengths and your weaknesses.”

But for Mr. Bennett, who as a child actor charmed Harrison Ford and Bruce Willis and earned the nickname Jimmy Two-Takes because he rarely flubbed his lines, the 2013 hotel-room encounter was a betrayal that precipitated a spiral of emotional problems, according to the documents.

Ms. Argento, who lives in Rome, subsequently turned to Ms. Goldberg — a prominent lawyer for victims of online attacks — to handle the case. (Mr. Hofstetter is now handling the estate of Mr. Bourdain, who killed himself in June. Although Mr. Bourdain helped Ms. Argento navigate the matter, neither Mr. Hofstetter nor Kimberly Witherspoon, Mr. Bourdain’s longtime agent and now a spokeswoman for his wife, Ottavia Busia, from whom he was separated, would comment for this article.)

Mr. Bennett’s notice of intent asked for $3.5 million in damages for the intentional infliction of emotional distress, lost wages, assault and battery. Mr. Bennett made more than $2.7 million in the five years before the 2013 meeting with Ms. Argento, but his income has since dropped to an average of $60,000 a year, which he attributes to the trauma that followed the sexual encounter with Ms. Argento, his lawyer wrote.

In October, a month before Mr. Bennett sent his demand for money, The New Yorker published an article by Ronan Farrow that included Ms. Argento among 13 women who accused Mr. Weinstein of harassment and rape.

Ms. Argento, whose father, Dario Argento, is a noted director of Italian horror films, began her acting career as a child. She went on to win two David di Donatello Awards, the Italian equivalent of Oscars, and has directed films, written a novel and recorded music.

After she spoke out about Mr. Weinstein, Ms. Argento quickly emerged as a powerful voice for women who have been mistreated by men. In May, she gave a riveting speech at the Cannes Film Festival in which she called the festival Mr. Weinstein’s “hunting ground.” She said he had raped her there in 1997, when she was 21.

The relationship with Mr. Weinstein continued for years afterward and sometimes included sex, The New Yorker reported. Ms. Argento, who had acted in a movie Mr. Weinstein produced, told the magazine that she feared angering him. It was a complicated situation in which she said she felt powerless. “After the rape, he won,” she told Mr. Farrow.

Mr. Bourdain, long a fan of her father’s work, met Ms. Argento when he was shooting an episode of his CNN show “Parts Unknown” in Rome in late 2016. The two became a couple, and Mr. Bourdain became her champion as she emerged as a leading figure in the battle against sexual assault and harassment, speaking at conferences and at Harvard.

For Mr. Bennett, seeing Ms. Argento present herself as a victim of sexual assault was too much to bear, his lawyer wrote, and called up memories of their hotel reunion. “His feelings about that day were brought to the forefront recently when Ms. Argento took the spotlight as one of the many victims of Harvey Weinstein,” Mr. Sattro wrote in the notice of intent to sue.

Ms. Argento, who is divorced and has two children, was both a mentor and a mother figure to Mr. Bennett, the document says, and the two were intermittently in contact as he grew up. “Jimmy’s impression of this situation was that a mother-son relationship had blossomed from their experience on set together,” Mr. Sattro wrote.

Mr. Bennett began acting at age 6, when he was cast in a commercial for a Dodge Caravan. He went on to appear in dozens of other commercials, and secured roles in several television shows. His prolific movie career started in 2003 with “Daddy Day Care,” which starred Eddie Murphy.

Mr. Bennett was 7 when he was cast in “The Heart Is Deceitful Above All Things,” a 2004 film Ms. Argento directed, starred in and helped write.

In interviews and subsequent social media posts between the two over the years, they referred to each other as mother and son.

On May 9, 2013, the day they met for a reunion in her room at a Ritz-Carlton in Marina del Rey, Calif., she posted on Instagram: “Waiting for my long lost son my love @jimmymbennett in trepidation #marinadelrey smoking cigarettes like there was no next week.”

Mr. Bennett responded, “I’m almost there!:)”

Mr. Bennett, who has an eye condition that prevents him from driving, arrived at Ms. Argento’s hotel room that morning with a family member, according to his notice of intent.

The document lays out Mr. Bennett’s account: Ms. Argento asked the family member to leave so she could be alone with the actor. She gave him alcohol to drink and showed him a series of notes she had written to him on hotel stationery. Then she kissed him, pushed him back on the bed, removed his pants and performed oral sex. She climbed on top of him and the two had intercourse, the document says. She then asked him to take a number of photos.

Later that day she posted a close-up of their faces on Instagram with the caption, “Happiest day of my life reunion with @jimmymbennett xox,” and added that “jimmy is going to be in my next movie and that is a fact, dig that jack.” That post and others were included with the notice of intent, along with three photos apparently taken by Mr. Bennett that depict him and Ms. Argento in bed, their unclothed torsos exposed. (Only one of the photos taken in bed shows both their faces.)

The two had lunch, and Mr. Bennett headed home to Orange County, where he lived with his parents. As he was driven home, according to his claim, he began to feel “extremely confused, mortified, and disgusted.”

That same month, he confronted his mother and stepfather over the state of a trust into which some of his earnings as an actor had been deposited, according to a lawsuit he filed in Orange County Superior Court in October 2014.

Mr. Bennett claimed his parents had barred him from the family’s house and kept his possessions, and over the years had cheated him out of at least $1.5 million in earnings. He said he was broke and two months behind on his rent. The case was settled in December 2014, but the terms were not disclosed.

In the agreement between Ms. Argento and Mr. Bennett, she agreed to pay him $380,000 over the course of a year and a half, starting with an initial payment of $200,000 that was made in April, according to a letter to Ms. Argento in which her lawyer, Ms. Goldberg, outlined the terms of the deal.

The agreement does not prevent either party from discussing it. In the letter, Ms. Goldberg explained that California law does not allow nondisclosure agreements in civil contracts involving the types of allegations made by Mr. Bennett.

One alternative, Ms. Goldberg wrote, would be to work around the California law by using New York lawyers and arguing that the laws of New York govern the agreement.

“Ultimately, you decided against the non-disclosure language because you felt it was inconsistent with the public messages you’ve conveyed about the societal perils of non-disclosure agreements,” she wrote to Ms. Argento.

“At the very least,” Ms. Goldberg added, “he is not permitted to bother you for more money, disparage you or sue — so long as you comply with your obligations in the agreement.”

Although it is unclear whether Mr. Bennett and Ms. Argento have spoken since the payment was made, Ms. Argento seems to remain supportive. On July 17, she added a “Like” to a moody portrait of himself he had posted on his Instagram account. The account has since been scrubbed of much of its content.