Matthew Flinders unexpectedly met the French ship Le Geographe, commanded by Nicolas Baudin. It was 8 April 1802. He had completed his exploration of Saint Vincent Gulf, re-provisioned and filled his water casks on Kangaroo Island and began to follow the coast to the south-east. Two ships in previously unexplored waters faced each other anxiously: their countries were at war. It was possible that the flags of truce might be dishonoured, so both captains were cautious. Flinders was aware that the French were exploring these waters, but the French captain did not know about Flinders's expedition which had left England after the French had sailed.

Matthew Flinders sailed from Portsmouth in HMS Investigator on 18 July 1801 to explore New Holland's (Australia's) unknown southern coast. By 27 January 1802, the Investigator was near the head of the Great Australian Bight. From February to March 1802, the British crew surveyed Spencer Gulf, explored Kangaroo Island, and charted Saint Vincent Gulf. In April the Investigator revisited Kangaroo Island, and on April 8 and 9, unexpectedly met the French expedition under the command of Nicolas Baudin at the location which became known as Encounter Bay. Despite their countries being at war, the captains exchanged information in a spirit of cooperation. Flinders continued to journey eastwards, leaving present day South Australian waters on 19 April, and reaching Port Jackson in May 1802. After the Investigator had been refitted and the crew rested, the English expedition sailed north to survey the eastern coast of the continent, adding to James Cook's earlier charts, and then chart the Gulf of Carpentaria.

The pressing need for further ship repairs forced Flinders to sail to Timor. He stopped his survey of the north Australian coastline at Wessel Islands. The Investigator then continued on around the western and southern coasts of New Holland, arriving back in Port Jackson [Sydney] in June 1803, thereby completing the circumnavigation. The Investigator was deemed unseaworthy, so Flinders sailed in the Porpoise to return to England, only to be shipwrecked at Wreck Reef. Using the Porpoise's cutter, Flinders returned to Port Jackson and arranged the rescue of the crew. In a second attempt to return home, Flinders set out on the Cumberland, but as this ship required repair, he was forced to seek assistance at Ile de France [Mauritius].

France and England had resumed war, and the Governor General of Ile de France detained Flinders for the next 6 years. During this period Flinders prepared his charts and in a letter to Sir Joseph Banks, championed the name 'Australia' for the entire southern continent, rather than 'Terra Australis' or 'New Holland'. Flinders finally gained his freedom, leaving Ile de France in June 1810 and arriving back in England in October of that year. His account of the expedition A voyage to Terra Australis, with Atlas, was published on 18 July 1814. Flinders who had been gravely ill for some time, died the following day.