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Florence Parly personally took the decision to drop the bilateral meeting with British Defence Secretary Ben Wallace, the sources said.
The French defence ministry could not be immediately reached. The British defence ministry declined comment.
The sources confirmed an earlier report in the Guardian newspaper that the meeting had been cancelled.
The scrapping of the multibillion-dollar submarine contract, struck in 2016, has triggered a diplomatic crisis, with Paris recalling its ambassadors from Washington and Canberra.
France claims not to have been consulted by its allies, while Australia says it had made clear to Paris for months its concerns over the contract.
French President Emmanuel Macron and United States President Joe Biden will speak by telephone in the coming days to discuss the crisis, the French government's spokesman said on Sunday.
British Prime Minister Boris Johnson is seeking to smooth relations with France, following the joint, Bloomberg News reported.
"We are very, very proud of our relationship with France", Johnson told reporters on his way to New York, according to the report. "Our love of France is ineradicable."
The United Kingdom and France are working on joint military operations in Mali and the Baltic states and are also working jointly on a simulated nuclear testing programme, the report added, citing Johnson.
Meanwhile, Australian Trade Minister Dan Tehan says he will seek a meeting with his French counterpart to ease tensions over Canberra's decision to scrap the $US40 billion (NZ$56 billion) submarine deal.
Australia last week said it would end the deal with France's Naval Group to build a fleet of conventional submarines and would instead build at least eight nuclear-powered submarines with US and British technology.
France was infuriated and said its relationships with Australia and the United States are in crisis.
Tehan said he was confident the row would not spill over and impact trade, but added he would seek a meeting with his French counterpart when he is in Paris for an Organisation for Economic Cooperation and Development meeting in October.
"I will be very keen to touch base with my French counterpart while I'm in France," Tehan told Australian Broadcasting Corporation radio on Monday.
Australian and EU officials are scheduled to hold their next round of talks over a trade deal on October 12.
The Australian-French bilateral tensions come as Prime Minister Scott Morrison travels to Washington for a meeting for the Quad group of countries - which includes India, Japan, the United States and Australia - later this week.
While France has been the most vocal critic of Australia's defence deal, China - which is seen as the catalyst for Australia's decision to build a new fleet of submarines - has also condemned the trilateral pact.
Australia's relations with China have deteriorated over the past two years after Australia banned Chinese tech giant Huawei from involvement in its nascent 5G broadband network and called for an enquiry into the origins of the novel coronavirus.
China has responded by impeding imports of Australian goods and it ceased all ministerial communications.
But Tehan said if China would like to join the Comprehensive and Progressive Agreement for Trans-Pacific Partnership trade bloc it would have to engage with Australia.