From what was described in the timeline so far,Antipodea was a huge benefit to France,and was prospering economically. I don’t think they would have been a burden.
As for jaded,the only way plausible for Antipodeans to suddenly call for independence would be for France to deliberately sacrifice Antipodean troops to protect Metropolitan French troops.I think that is the only reason why Antipodea would demand immediate independence.But you will probably have to make French commanders hold the idiot ball to do that. Even the British,who clearly saw the Australians as second rate troops didn’t actually do that. I do think it’s possible for that to happen,but somewhat unlikely.
Given that the Antipodean government was modeled on the Dominion of Canada,I do think that they already have sufficient autonomy.