The expedition began with the blessing of the most powerful man in France. In March 1800, Napoleon Bonaparte, then First Consul, received Baudin and a delegation of scientists and approved a voyage "to the coasts of New Holland" for the express purpose of geography and natural history. It was, on its face, a mission of pure science. Two ships sailed from Le Havre that October: Géographe under Baudin and Naturaliste under Jacques Hamelin, carrying an unusually large company of zoologists, botanists, gardeners, and artists, among them the young naturalist François Péron and the artist Charles-Alexandre Lesueur. The ambition was openly competitive. The French meant to match, and if possible surpass, the achievements of Captain Cook.

Science came at a punishing price. Delays in Mauritius meant the ships did not reach the Western Australian coast until May 1801, and at Geographe Bay they lost a longboat and a sailor, Timothée Vasse, whose name still marks the country there. Sailing north, the two ships became separated and did not reunite until Timor. Dysentery and fever raged through the crews. They pressed on regardless, charting the entire east coast of Tasmania and conducting careful, respectful studies of the Indigenous Tasmanians, with whom they kept peaceful relations and whose lives they recorded in ethnographic detail that historians still value. Of the twenty-four scientists and artists who set out, illness forced ten ashore in Mauritius before Australia was even reached, and five more died along the way. Only six of the original scientific company would ever see France again.

At Encounter Bay, Flinders told Baudin about his recent discoveries, including a large island offshore where the crews could find fresh food. The French explored that coast in turn, and Baudin's expedition became the first to circumnavigate and chart much of Kangaroo Island, which is why so many of its capes and bays still carry French names today. In 1803, members of the Géographe came ashore at what is now Penneshaw and carved an inscription into a rock: an expedition of discovery by Captain Baudin. To save it from the weather, the original stone now sits in a visitor centre, while a replica rests on the foreshore beneath a small concrete dome that has been a local landmark since 1906.

The voyage carried a shadow purpose. Researchers from the University of Adelaide have found that, during the expedition, Baudin drew up a report for Napoleon on how the British colony at Sydney Cove might be invaded and seized, and the French openly noted the town's defences and the discontent of its Irish convicts. Whatever its secret ambitions, the expedition's scientific haul was staggering: more than 2,500 species new to European science, over 200,000 specimens deposited in the museums and gardens of Paris, and live plants and animals sent to Empress Josephine's gardens at Malmaison. Baudin himself never enjoyed the acclaim. Worn down by the journey, he died of tuberculosis in Mauritius on 16 September 1803, and the ships reached France the following March without him.

History was not kind to Baudin's memory, and his crews were partly to blame. François Péron and Louis de Freycinet, who lived to write up the voyage, gave their late commander little credit. When Freycinet published the expedition's great chart in 1811, it was the first printed map to show the complete outline of Australia, an achievement built on Baudin's leadership yet stamped with another man's name. The French had also slapped the label Terre Napoléon across much of the southern coast. Those names faded; Flinders' did not. But the science endured, and the encounter endured, and the strange, generous truce between two enemies on a wild coast remains the voyage's finest legacy.