The Bésixdouze was a sea vessel belonging to the science expedition, a group of six French researchers including Danielle Rousseau. It wrecked near the Island during a storm on November 18, 1988 while the expedition was attempting to locate the source of a voice repeating the numbers over a radio transmission. Little is known about the vessel, but it carried at least one inflatable life raft, which presumably saved the researchers during the storm that had caused them to abandon ship. ("The Little Prince")
Danielle Rousseau claimed the ship ran aground, presumably on the Island, but all that is seen of the ship is its raft and washed up cargo. This leads to one of many inconsistencies between her story and actual events. However, her map denotes a spot on the atoll with a drawing of a sinking ship, labelled "the site of the sinking" (le lieu du naufrage), likely the spot where her ship went down.
Bé-six-douze is French for B-six-twelve. In The Little Prince by Antoine de Saint-Exupéry, the title character lives on Asteroid B-612.