He said the government could also make a "direct contribution", and the idea has "many precedents".

But Prime Minister Scott Morrison was lukewarm on the idea of a fund when asked about it on Adelaide's 5AA radio.

"Well, I know people would like to do that and there will be opportunities to do that," Mr Morrison said, without endorsing the idea of a fund.

French President Emmanuel Macron has vowed to rebuild the famed gothic cathedral in the wake of the devastating fire, in which Notre Dame lost its roof and spire.

"We will rebuild this cathedral all together Mr Macron," Mr Macron said on Monday night Paris time.

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"Starting tomorrow, a national subscription will be launched, and well beyond our borders we will appeal to the greatest talents," Mr Macron said, "And there are many who will come to contribute and rebuild [with] us."

Opposition leader Bill Shorten — who remembered using the Cathedral as a navigational landmark as a backpacker — told reporters in Melbourne he supported Mr Turnbull's proposal, saying Australia should contribute to a restoration fund.

"Notre Dame doesn't just belong to Paris or France, it belongs to the world. I think we, all of us who've enjoyed that architecture, that history, we too should perhaps rally around and help Paris and Notre Dame," Mr Shorten said.

Donations to the fund would be channeled to the reconstruction of Notre Dame, which has already attracted high-profile offers of support.

The billionaire Francios-Henri Pinault, chairman of the company that owns luxury brands Gucci, Yves Saint Laurent, Balenciaga and Alexander McQueen, and his father have pledged to donate 100 million Euro ($143 million) to the rebuilding effort.