Captain Adeline Champagnat, a senior member of the police cyber crimes unit, said the 25-year-old man gained access to passwords of Twitter administrators and used them to try to break into the accounts of U.S. politicians and stars.
"He didn't get as far as their personal accounts. But he had gained control of Twitter," she told Reuters Television in an interview.
She said the FBI had tipped off the French police in July last year that one or more people were trying to get access to Twitter and had gained control of the social network.
That enabled them to create and delete accounts and steal confidential information.
The hacker, who went by the online name of HackerCroll, is under arrest in the central French town of Clermont Ferrand.
He was known to have carried out minor internet fraud but in this case was driven by the thrill of the challenge and appeared to be more interested in the private life of his victims than on obtaining sensitive data, Champagnat said.
"His aim wasn't to make money. It was simply to show that he was able to access accounts of Twitter members. And the best proof of that is that he did screen grabs of certain confidential data which he tried to post on blogs that are reserved for pirates or hackers," she said.
She said several FBI agents were currently in France to help their French counterparts carry out searches.
"The collaboration was very good with the FBI and it's always very good with the FBI, because there's a real exchange of information. It's good cooperation to arrest the offender," she said.
(Reporting by Yann Tessier; editing by Tim Pearce)