Watson was arrested in Greenland on Sunday, and pending a decision on his possible extradition to Japan, he will be held until 15 August.
His ship had docked to refuel on its way to "intercept" Japan's new whaling factory vessel in the North Pacific, according to the Captain Paul Watson Foundation (CPWF).
French screen legend turned animal rights activist Bardot told Le Parisien in an interview published on Monday that "the Japanese government... launched a global manhunt" against Watson who was "caught in the trap".
"We must do everything to save Paul," she said.
Watson, who featured in the reality TV series "Whale Wars", founded the Sea Shepherd and the CPWF organisations, and has drawn attention for direct action tactics, including confrontations with whaling ships at sea.
CPWF said it believed his arrest was in connection with an Interpol Red Notice related to Watson's previous anti-whaling activities in the Antarctic.
Japan's government made no comment but a spokeswoman for the Japanese coastguard told AFP on Monday it was aware of the arrest.
"The coastguard will continue to take appropriate steps based on coordination with related entities," the spokeswoman said.
The Red Notice was issued in 2012, with an Interpol statement at the same saying Watson was wanted by Japan on charges of causing damage and injury in two incidents in the Antarctic Ocean in 2010 against a Japanese whaling ship.
