"An investigation to determine the cause of death was opened on Monday evening following the discovery," the office said, adding that an autopsy will be carried out.
Siad's name appeared thousands of times in the Epstein files released by the US government. He had previously denied any knowledge of the threat that Epstein posed.
During one e-mail to Epstein released in the files, Siad wrote in badly-spelled English: "In This busyness I feel like fisherman some time I cache quick, some time no fish".
Ahead of a BBC investigation on the subject published on 18 July, Siad's lawyer had said he was not available for comment, but in a recent CNN interview, Siad said he did not know the women were being abused by Epstein: "I trusted him, I believed this guy is a professional person."
Siad himself was the subject of several complaints in France, including allegations of rape, with the first filed in February. He denied wrongdoing in multiple recent media interviews, telling BFMTV in May: "I have never raped anyone in my life."
Lawyers for the former model who made the first complaint said they were "stunned" by his death.
"We are at a loss for words to describe the anger and sadness we feel," they said, with the sadness for their clients "now denied a criminal trial".
The lawyers said they feel "immense anger toward the Paris Public Prosecutor's Office, which announced last February that it was opening an investigation into Jeffrey Epstein's French accomplices".
They accused the office of "scandalous" inaction which they said "demonstrates the public authorities' contempt for victims of sexual crimes, even when these crimes are linked to the human trafficking network established by Epstein and his accomplices".
Another former model who had given a deposition to police in June as part of the investigation into Siad told the BBC that his death meant any information he may have had about Epstein was now lost.
"An important link in the chain has just vanished into thin air, without there even having been a chance to recover the information Daniel Siad might have possessed, given that he was never questioned," she said.
"Too much time has been lost... and it is yet another way for the leads to go cold. I hope we won't have to wait another seven years to see his home searched, even though I think it is already too late."
"My clients found the strength to break a particularly heavy silence, given Daniel Siad's ties to Jeffrey Epstein," she said. "They faced every stage of the proceedings with remarkable courage."
"It is deeply regrettable that the slow pace of the investigation resulted in his death before he could be questioned or taken into police custody, thereby depriving the victims of a crucial step in their pursuit of truth and justice."
The 76-year-old had been held in custody for more than a year as he was investigated on suspicion of the rape of minors and trafficking of minors for sexual exploitation. Brunel had denied any wrongdoing.
