To be honest, I don't know the chances, but here are the following facts, hopefully they give good picture on topic:
The continent was spotted by various people before James Cook - collected evidences are from the related wikipedia page's sources:
K.G. McIntyre (1977) The Secret Discovery of Australia; Portuguese
discoveries 200 years before Captain Cook. Souvenir Press, Medindie,
South Australia The discovery is claimed by Portugal long before
An another claimant is a less known French sailor Binot Paulmier de Gonneville who stated that from the Cape of Good Hope (South-Africa) he sailed 6 weeks to east and hit a new coast, but the commonly accepted that he didn't reach Australia but nowadays Brazilia.
Later Dutch sailors reached Australia, but the first one who took Australia seriously was Captain Cook, so they claimed the whole territory of Australia. Of course there were competitors.
the west coast of the continent (later Western Australia), which Louis de Saint Aloüarn officially claimed for France in 1772 — even though it had been mapped previously by Dutch mariners.
Take a note, France was involved to American freedom fight, had cultural renewal by Enlightment, and of course the 1789 revolution happened, then Napoleon focused all the resources to Europe, they even sold Louisiana to finance war. We can say, the focus wasn't on Australia in France to press any claims, so Great Britain had relatively a green light to do whatever they want there.