doesn't need to know you're a dual citizen. Even if they do, they won't care which passport you choose to use. The US government even says you can just choose which passport to use (https://help.cbp.gov/app/answers/detail/a_id/1096/~/esta---eligible-passport,-country-of-issuance,-citizenship).
The fact that you live in France does not mean that the US will require you to travel as a French citizen. The only country where you must present yourself as a French citizen is France.
It is fine to leave France with your French passport and enter the US with your Australian. In short, don't worry about it.
EDIT: It has come to my attention that the ESTA application asks you to disclose all of your citizenships. So the statement that "US immigration doesn't need to know you're a dual citizen" is not true.