David Geoffrion, working for Canal+, was detained by pro-Russian gunmen at a military installation in the Ukrainian town of Simferopol, said a French source with knowledge of the situation who asked not to be named.
Tension in the Black Sea peninsula has been growing since pro-Russian separatists took control of the regional parliament, declaring Crimea part of the Russian Federation and announcing a referendum for March 16 to confirm this.
In little more than a week, Russian forces have taken over military installations across Crimea, home to the Russian Black Sea fleet. Unidentified men fired in the air on Monday as they moved into a Ukrainian naval post.
"David Geoffrion was arrested. He was in Ukraine to do a documentary," the Canal+ spokesman said.
France's foreign ministry could not immediately confirm the information.
Paris-based media watchdog Reporters Without Borders said on Monday it was alarmed by the steady escalation in violations of journalists' rights in Crimea after two Ukrainian journalists were arrested.
Separately, speaking ahead of a planned visit to Moscow on Tuesday, French Foreign Minister Laurent Fabius said the only way to resolve the "very difficult and dangerous situation" was through dialogue, but time was running out.
"This referendum in Crimea is against international law and the choice is not being left to anybody. It's the choice of yes or yes," he said at a news conference with his Irish counterpart.
"I am planning to go to Moscow on Tuesday with (Defence Minister) Le Drian, but only if it is useful."