Robert,

I'm pretty sure that the gulf was named by Nicholas Boudin who was sent by Napoleon to explore Australia. While there, the French expedition met an English one in 1802 and explored the coastline together.

An article is available in the January 2003 History Today Magazine

http://www.historytoday.com/dt_main_allatonce.asp?gid=19115&aid=&tgid=&amid=19115&g19115=x&g19104=x&g30026=x&g20991=x&g21010=x&g19965=x&g19963=x