The couple is said to have avoided being spotted by boarding the New Year’s Eve British Airways flight earlier than other passengers.
They headed straight to the back of the plane and sat next to the rear toilets, according to the Daily Mail.
The newspaper said that Prince Harry sat by the window with a baseball cap pulled over his face, with Ms Markle next to him in a black beanie hat.
They were joined by three “edgy and nervous” bodyguards, with the group taking up three rows of economy seats on both sides of the aisle.
When the pair touched down in France they were greeted by armed officers from the French border police.
Meanwhile sources told the Mail that France’s elite Service de la Protection will guard the couple during their stay.
Kensington Palace declined to comment.
Prince Harry, 33, and 36-year-old Ms Markle, who have enjoyed a whirlwind romance after being introduced by mutual friends in London, are to marry on May 19 at Windsor Castle.
The couple revealed they were engaged on November 27 last year, with Prince Harry popping the question over a roast chicken dinner.