Jones said Barnard, from the village of Ogmore Vale, Bridgend county, held the culprit until police arrived “and then gave the handbag back to the traumatised granny”.
“Then, he jogs over to our film panel, sits down, calm as can be [and] regales the audience with tales from the film shoot. Folks, I swooned,” said Jones, who is the son of pop icon David Bowie.
Annecy festival said the incident occured in the city centre, not on the festival site, about one hour before the panel event.
Annecy Municipal Police has been contacted for comment.
Rogue Trooper is the latest project by Jones, whose previous work includes Source Code and Warcraft.
Barnard plays the title role in the new film, which premiered at the festival and will be released later this year.
Rogue Trooper, based on a popular UK sci-fi comic series, is an animated science fiction feature by Rebellion and Liberty Films, which tells the story of a “genetic infantryman” who finds himself the sole survivor of an invasion force.
Desperate to track down the traitor who sold him and his comrades out, the super soldier is accompanied by three killed-in-action squad mates, whose personalities have been stored in his gun, helmet and backpack.
Written and directed by Jones, the cast also features Jack Lowden of Slow Horses, Inside No 9’s Reece Shearsmith, comedian Diane Morgan, Game of Thrones’ Sean Bean and Sex Education star Asa Butterfield.