This is a program that has not gone unnoticed to Baptist brother, founder of Planet Ride (here).

And yes, his maternal surname is Barret, and there is indeed a Jeanne in her ancestry:
Jeanne Barret (1885-1969), a very erudite governess of children of a diplomat named in Argentina, followed the family there. Returning to France in the 1930s, her savings placed in Argentine funds lost during the Peronist revolution, she ends her life with few resources, but full of life and rich with a solid humour, proud prerogative of the Barret family!

But it is from another Jeanne Baret (or Barret, the spelling is not fixed) of which the show speaks.
Born in 1740 in a small village of Burgundy, a family of peasants, and undoubtedly illiterate, she was hired as a servant at the Doctor Philibert Commersion, a learned botanist.
Very quickly, he is seduced by the intelligence and the alertness of the young woman who is passionate about her herbariums and all kinds of knowledge, she learns very quickly, and becomes her assistant, her indispensable right arm…
Two years later, he was appointed botanist of King Louis XVI, and as such was to embark on a voyage to the Southern lands: to accompany Monsieur de Bougainville as His Majesty's Botanist and to do, as he wrote in his will Before leaving: "Observations on the three reigns of nature in all the countries where the officers will lead me; So God help me… »
The couple became inseparable, both in life and in the study. An order prohibits women from embarking on Royal Navy ships. To this, Jeanne disguised herself as a valet, and embarked for the expedition on 6 February 1767, at Rochefort. Two boats are chartered: the sulking and the star.

Life on the boat is not the easiest… Indeed, there are only men on board and Jeanne must show a great deal of finesse and prudence to keep her secret. He is not a sea-foot, he is cared for by his servant "Jean Baret"… As for Jeanne, to appear a man, she works like a frenzied in order to dismiss suspicions. Despite all his efforts, noises run on the boat, which Bougainville feigns to ignore.
The crossing to Montevideo lasts three months. The star continues on its way to the south, and the expedition arrives in Patagonia, which can finally botanize in the company of his servant.
The suspicions have calmed down, Bougainville writes in his diary: "How to recognise a woman in this tireless baret, a botanist already very exercised that we have seen follow his master in all his herborisations and carry even, in his arduous steps, the Mouth provisions, weapons and plant books with courage and strength that earned him the nickname of Beast of Sum? »

The expedition continues on its way to the Strait of Magellan. On January 26, 1768, the star entered the Pacific. Equipped with more or less exact maps, Bougainville avoids Easter Island and continues its road to finally wet off Tahiti, greeted by a hundred canoes with pendulum.
The cohabitation between Tahitians and French is peaceful: the latter were able, after bitter negotiations, to set up a camp ashore to treat the sick. It was then that the episode of April 7 occurred.
Until then, the sailors knew only one word of the Tahitian vocabulary "Tayo" which means "friend". But that morning, she docked on the island with her servant for Botanize. No sooner have they set foot ashore than a crowd of excited natives circling them shouting "Aryan!" Aryan! ». A native seizes the young servant and flees with his prey under the eyes amazed of the poor…
It took the presence of the spirit of an officer who was there by chance and who, from his sword "made the whole mob stand aside and frightened the courcié who let it take."
The incident was quickly mastered, but on the evening of 7 April, the star sailors learned a new word in Tahiti: "Woman".
Jeanne is now on board while Botanize continues on the island without much conviction. Obviously Jeanne has become more than indispensable to her work.
The expedition continues on its way to the Indian Ocean. In November the couple landed with all its collections of natural history in Port Louis, on the island of France (present-day Mauritius), important French counter whose Intendant is then another botanist: stone pepper.
There is no doubt that this is a disciplinary measure, but also a form of protection with regard to the sanctions that Bougainvillier and commersion can incur when they return to France. Jeanne continues her work as assistant and follower for Botaniser in Madagascar and Bourbon Island (Réunion) in 1770-1772.
The health of the swamp remains fragile, he dies, leaving Jeanne without a resource. She's 32 years old. It is no longer entitled to any consideration or assistance whatsoever. Jeanne opened a billiards-cabaret, met Jean Bernate, a naval soldier with whom she married on May 17, 1774.
This marriage with a member is the only way to obtain a repatriation permit.
She returned to Paris 1776 with more than 30 sealed crates containing 5000 species of plants collected during her journey around the world, 3000 of them are new. Among them, named by Commersion, are the famous "Bougainvillier", and a shrub: "Baretia bonnafidia".
Jeanne sends this treasure to the King's Garden. These collections will join those of the Museum of Natural History where we can always consult the manuscripts of commersion.
Jeanne received the share of the inheritance bequeathed to her by Philibert, and on November 13, 1785, she was honoured for her commitment to the expedition of Monsieur de Bougainville. His work with the Swamp is officially recognized by the King who grants him a pension.
Jeanne Baret has done well around the world. Part of Rochefort in 1767, she returned to France nine years later. She is the first woman to have done such a feat.

Sources:
The Jeanne Baret case, by Nicole Creystey, associate professor
of natural sciences at the IUFM.
http://www.pays-de-bergerac.com/pages/culture-patrimoine/personnages-celebres/jeanne-baret/
Https://fr.wikipedia.org/wiki/Jeanne_Barret