French environmental campaigners had called for the shipment, sent by France-based nuclear company Areva, to be stopped.
The BBC Shanghai is due to reach Australia by 27 November.
French officials said an inspection had revealed no problems that could prevent the ship from sailing.
The 25 tonnes of nuclear waste comes from Areva's reprocessing plant in Beaumont-Hague, near the port of Cherbourg, from where the ship set sail on Thursday.
Yannick Rousselet, of Greenpeace France, said the BBC Shanghai "should not be used" to transport the nuclear waste.
Nathalie Geismar, of French environmental group Robin des Bois, said that other ports had found a "staggering number of flaws" in the 14-year-old ship.
Shortly before the cargo ship set sail, French Green MP Denis Baupin tweeted (in French) that Areva was "using a dustbin ship to carry waste, without any serious inspection".
Letzte Einträge: Life is too short , so laugh