The Chinese state aviation regulator, CAAC, could not be immediately contacted for comment.
The French Embassy said that three Chinese carriers, Air China, China Eastern Airlines Corp and China Southern Airlines Co, were each authorized to operate weekly flights between Chinese cities and Paris.
He said that, under a reciprocal agreement of June 12, Air France had been authorized by Beijing to make three flights a week to China.
But the embassy said that, in practice, the Chinese authorities had authorized only one Air France flight per week.
He said France was applying intense diplomatic pressure to get the green light from Beijing for additional flights. In the meantime, he advised travelers to prepare for an interruption in air links between the two countries.
Passenger flights between France and China were suspended earlier this year due to the COVID-19 pandemic.
Report by Christian Lowe in Paris and Stella Qiu in Beijing, edited by Ed Osmond
Our standards:Principles of the Thomson Reuters Trust.