It is your responsability to update your Australian visa when you get your new French passport!
After you receive your new French passport, you will need to update your Australian visa at the Department of Immigration and Border Protection. You should do this as soon as possible after receiving your new passport.
You can either go in person to the Department of Immigration and Border Protection, with your new French passport, or you can submit the required form by post, if it is not urgent. You also have the option of completing an online form. Click here for more information.