No genuine science expedition would willingly take along a woman who was seven months pregnant.
Danielle was not seven months pregnant when the expedition left. According to the timeline, Alex was born in April 1988, and they sailed from Tahiti the previous November, when Danielle would have been only a couple months pregnant. They would have departed from France even earlier than that, probably October. It is possible/likely she did know she was pregnant until the exhibition was underway.
The French expedition has nothing to do with Widmore or the DHARMA Initiative but is a third-party attempt to discover the Island. The fact that the team is armed with rifles indicates they were doing more than charting ocean currents. France has several colonies and territories in the South Pacific, and it's possible someone in one of them heard the Numbers just as Leonard Simms and Sam Toomey once did. This information eventually came to the attention of someone who knew about DHARMA and the Island, who then dispatched the expedition to try and locate the Island. At least one of the crew members is aware of the real mission, even if the others are in the dark.
Maybe the third party that could've sent the team was Eloise. She would've been exiled/gone from the Island at this point, seeing as Widmore was now the leader in 1988.
The science expedition are 'innocent' in the sense that none of them had prior knowledge of the Hanso Foundation, DHARMA, Widmore or The Others. Like Leonard and Sam, they somehow heard the transmission. It was likely they were brought to the Island through the influence of Jacob, as the members of the expedition were candidates.
Danielle was seven months pregnant when she landed, therefore when the events leading to her team's demise occurred two months later. She would close to giving birth. The Others caused these events to capture Alex.
Ben's instructions from Widmore were to kill Danielle. They did not know there was a baby until Ben returned with her, which angered Widmore, who thought he should have killed her too.
The name Bésixdouze appears to be a reference to Antoine de Saint-Exupéry's Le Petit Prince and, thus, the name of the episode. In the novel, the Little Prince comes from a planet/asteroid known as "B612", or in French, bé six-cent-douze.