The Love Productions show will be renamed The Great Bake Off and will be shown on commercial station M6.
The Great Bake Off will be produced by BBC Worldwide's production base in France and is due to air later this year.
"Having crossed the English Channel to the spiritual home of the sweet tooth, this warm and authentic format... has all the crucial elements to be a showstopper," said Jean Louis Blot, Creative Director at BBC Worldwide Productions France.
He added: "When it comes to The Great Bake Off, the proof is in the pudding!"
So far, the amateur baking contest - featuring Mary Berry and Paul Hollywood - has been licensed to and aired in six countries, including Australia (Nine Network), Poland (TLC), Belgium (VTM) and Ireland (TV3).
The Great Bake Off also airs in Scandinavia on TV4, where it is the highest rating show in the channel's history. The Danish version, Den Store Bagedyst, is the most successful of all the new formats that have premiered this season on any Danish channel.
The Great British Bake Off - hosted by Sue Perkins and Mel Giedroyc - recently recorded an all time high of 4.8 million viewers for BBC Two, and registered 19.9% of the market share.
The third series of The Great British Bake Off continues on Tuesday (October 9) at 8pm.