A production of 42.9m hectolitres (hl) (944m gallons) is forecast for 2016, down from last year's 47.8m hl.
The harvest is expected to be down by about a third in the Champagne region.
Prices will rise, although one French wine trader said the Brexit effect would be a greater inflationary pressure for UK buyers.
Jean-Pierre Hourlier, who sells mid-market French wines in the UK, said: "Prices are going up across the board because of the euro and the impact on transport because of Brexit."
