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".
The scheme involves a blacklist, which is shared with ad brokers whose software determines what ads go where.
香薰治療 But one expert said the effect on the sites' earnings might be "negligible".
Operation Creative was launched by the City of London Police's Intellectual Property Crime Unit (Pipcu) in the summer of 2013.
It led to the creation of the Infringing Website List (IWL) - a database of online services that the police have confirmed provide access to unauthorised content.
Hundreds of sites now appear on the list, which has not been made public. Owners are given a chance to remove illegal material before their platforms are included.
Two years on, Pipcu says there has been a 73% drop in advertising from the UK's "top ad spending companies" on the affected sites, which it suggests both reduces their income and removes their "look of legitimacy".
The figure is based on research carried out by Whitebullet - a firm that provides online intellectual property services.
It surveyed the ads placed on 17 sites that offer unauthorised access to TV shows, movies, music and games - both over a 12-week period between June and September 2013 and again between March and June 2015.