At least one of Mr. Epstein’s accusers has said that Mr. Brunel used his position as a modeling scout to procure minors for the billionaire, who once socialized with politicians, celebrities and Wall Street executives.

The investigation in France is still in a preliminary stage, and no one has been formally charged. Under French law, Mr. Brunel can be questioned by the police for up to 96 hours, depending on the charges being pressed, before he is either released or placed under formal investigation.

Corinne Dreyfus-Schmidt, a lawyer for Mr. Brunel, could not be reached immediately for comment. In a statement to The Guardian in 2015, Mr. Brunel vehemently denied involvement, “directly or indirectly,” in the accusations against Mr. Epstein. “I strongly deny having committed any illicit act or any wrongdoing in the course of my work as a scouter or model agencies manager,” he told The Guardian.

The Paris prosecutor’s office declined to comment on French news reports that before his arrest on Wednesday, Mr. Brunel was about to board a flight for Dakar, the capital of Senegal. Mr. Brunel was not under any type of judicial control and was free to travel.

Mr. Brunel started his career as a modeling agent in France, later becoming the head of Karin Models and founding MC2 Model Management. He expanded his career to the United States, where he met and befriended Mr. Epstein, often traveling and socializing with him before the two had a falling out as the sex-trafficking accusations against the billionaire emerged.

In court filings in a federal court in New York, Virginia Roberts Giuffre, one of Mr. Epstein’s accusers, alleged that Mr. Brunel would offer modeling jobs to girls — some as young as 12 — and bring them to the United States to “farm them out to his friends, especially Epstein.”

Ms. Giuffre also said Mr. Epstein sexually trafficked her to Mr. Brunel on “numerous occasions and in numerous places,” including the south of France, according to court records.

Messages apparently from phone calls scribbled on a notepad found in Mr. Epstein’s mansion in Palm Beach, Fla., appeared to show Mr. Brunel cryptically talking to his friend about underage girls, according to court records.

One message from 2005, titled “For Jeffrey From Jean Luc,” said: “He has a teacher for you to teach you how to speak Russian. She is 2×8 years old not blonde. Lessons are free and you can have your 1st today if you call.”

No criminal charges have been lodged against Mr. Brunel in federal court in New York.

But Mr. Brunel has faced direct accusations of abuse himself. In a 1988 “60 Minutes” exposé, several models accused him of inappropriate treatment, including drugging them and, in one case, rape.

Three former models also told The Guardian last year that he sexually assaulted them in the 1980s and ’90s in and around Paris.

Thysia Huisman, a former Dutch model who has accused Mr. Brunel of drugging and raping her in Paris in 1991, said she cried “tears of joy” after hearing about the arrest.

“I’m really happy that there is finally some movement in the case,” she said in a telephone interview. “I reported him to the police in September 2019, and I knew my case was past the statute of limitations, but I hoped it would motivate other women to come forward.”

Anne-Claire Lejeune, a lawyer who represents Ms. Huisman as well as three other women who have also accused Mr. Brunel of sexual misconduct, said Mr. Brunel’s arrest was “a very good first step” but she cautioned that he had yet to be charged and hoped that the prosecutors would hand over the inquiry to special magistrates.

Under French law, such magistrates have broad investigative powers and can place defendants under formal investigation. Not all preliminary investigations reach that stage, though, and prosecutors can drop cases if they do not uncover firm evidence of wrongdoing.

But some of the claims by Ms. Lejeune’s clients are blocked by statutory time limits for rape cases, which in France is 20 years. None of her clients have accused Mr. Epstein of wrongdoing.

Mr. Brunel is not the only figure in the French modeling agency to face rape accusations. Gérald Marie, who was president for 25 years of the European division of Elite Model Management, has also been accused by former models of rape and sexual assault dating back to the 1980s and 1990s.

Zoë Brock, a model from New Zealand who has accused Mr. Brunel of giving her drugs and trying to have sex with her in 1991 — when she was still a minor — said the arrest was a relief.

“I had given up on the French system completely,” she said in a telephone interview. “It’s incredibly exciting but I reserve my joy until there are any charges. I’ve learned through all of this that this takes a very long time.”

Benjamin Weiser contributed reporting and Amy Julia Harris contributed research from New York.