Federal Education Minister Dan Tehan has already expressed concern about left-wing protests shutting down events on campus,and has advocated new policies to force protesters to pay for security at functions they disrupt.
"We must ensure our universities are places that protect all free speech,even where what is being said may be unpopular or challenging,"Mr Tehan said.
"The best university education is one where students are taught to think for themselves,and protecting freedom of speech is how to guarantee that."
But some vice-chancellors view the push as redundant given their universities'existing policies to protect academic freedom and free expression.
Australian National University vice-chancellor Brian Schmidt said Mr French was a"good choice"to lead the review,but questioned whether it was needed.
"I expect the status quo to be retained - ANU,at least,is a place which welcomes discussions on issues made in good faith by our staff,students and invited experts,"he told Fairfax Media.
"I believe the same is true at almost all universities across Australia."