PARIS — Prosecutors in France said on Friday that they had opened a preliminary investigation into the scandal surrounding the disgraced financier Jeffrey Epstein, in connection with possible offenses such as rape, the sexual assault of minors and criminal conspiracy.

Rémy Heitz, the Paris prosecutor, announced the investigation after “exchanges” with the United States authorities, he said.

Mr. Heitz did not reveal whether his office had received any specific accusations involving Mr. Epstein, but said in a statement that the investigation would aim to “uncover potential offenses” committed either in France or against French victims abroad.

The prosecutor said he also would look into the possibility of French perpetrators. The statement did not name any individuals.