Oh yes. How did they get hold of New Caledonia, Tahiti, French Polynesia, or Wallis & Futuna?
The Sydney suburb of “La Perouse” was named after the French navigator Jean-François de Galaup, comte de Lapérouse (1741–88), who landed on the northern shore of Botany Bay west of Bare Island on 26 January 1788. Captain Arthur Phillip and the first fleet of convicts had arrived in Botany Bay a few days earlier. (Wiki https://en.wikipedia.org/wiki/La_Perouse,_New_South_Wales#History )
The encounter between the French and British was quite civil - but I doubt if either side were under any illusions as to why the others were there.
Before calling in at Botany Bay, La Perouse had been on an amazing expedition in his ships "L'Astrolabe" and "La Boussole" that covered: Cape Horn, Chile, Easter Island, Hawaii, Alaska, California (where he likened the Spanish missions to slave plantations), Macau, Korea, Japan and Sakhalin Island, then to Samoa (where a Samoan attack killed 12 and wounded 20 more) Tonga and Norfolk Island.
After Botany Bay La Perouse and his expedition completely disappeared.
In 1791, France sent out a search expedition led by Rear Admiral Bruni d’Entrecasteaux. This made for another dramatic expedition which (we now know) got quite close the the right area. But failed to find any real evidence of La Perouse. Then in 1825 Royal Navy Captain Thomas Manby encountered people from what is now one of the Solomon Islands who were wearing ornaments, swords and medals that could only have come from La Perouse. They told of a shipwreck a generation earlier. In 1826 Irish sea captain Peter Dillon was able to piece together the events of the tragedy. Both of La Perouse’s ships had been wrecked on Vanikoro Island. Some of the men were were massacred by the local inhabitants. Others built a boat from the wreckage and sailed away — never to be seen again. While two — “a chief and his servant” had remained but ”left” a few years before Dillon’s arrival.
Also in 1826 Jules Dumont d'Urville mounted another expedition - in a ship which he named "L'Astrolabe" in honour of La Perouse's ship. He proceeded to explore numerous places in the Pacific - naming many of them "Astrolabe" after his ship. This can be a bit confusing - as you might come a cross an "Astrolabe Reef" (say) and think, "Ah! La Perouse was here!" - when in fact it was named by Dumont D'Urville.