Some 70,500 people applied for asylum in France between January and October 2016, French refugees' agency Ofpra announced on Wednesday.
The total is 13 percent higher than the same period last year but marks a slower rise in demand than the first quarter of the year, when it hit 20 percent.
About 80,000 applications were made in 2015, a rise of 23.6 percent and officials predict this year's total will be about 90,000.
The lower rise may be the result of the EU's agreement with Turkey, which has caused a drop in the number of migrants coming to Europe via Greece.
Jungle, Guyana, Haiti may reverse trend
But the closure of the Jungle migrants' camp in Calais may push 2016's figure back up again.
Some 5,100 adults have been sent to centres where they are considering asylum applications in France, rather than in Britain which was their original aim.
Officials say that 85 percent of them are eligible.
The figures may also be affected by the reopening of an office in the French West Indian territory of Guyana.
It was closed in August after being swamped by applications, mainly from Haiti.
The number of applications accepted is likely to rise, according to Ofpra, which says that 37 percent of have received a positive response this year, mainly because the applicants came from countries hit by war or natural disaster.
The main countries of origin of applicants, including children, this year have been: