Bourgnon, 49, was on a private boat with tourists, who alerted the rescue services when he failed to come back on Wednesday at 1345 local time, the High Commission of the Republic in French Polynesia said in a statement.
A helicopter was on site at 1700 local time but Bourgnon has not been found.
Bourgnon won the Route du Rhum, a famous boat race from Brittany to the Caribbean island of Guadeloupe, in 1994 and 1998.
(Reporting by Daniel Pardon, writing by Julien Pretot; Editing by Ed Osmond)
