Future already publishes Official PlayStation2 Magazine in the UK, along with another PlayStation title, PSM2.
The deal also includes Joystick, Joypad and DVD Magazine, with the sale being approved by competition authorities in France. It marks the departure of Hachette Filipacchi, best known in the UK for women's magazines Red and Elle, from computer games publishing.
Future already publishes Official Nintendo magazine in France, along with PC Jeux, Jeux Video and Windows News.
Greg Ingham, Future's chief executive, said: "We are pleased to have received regulatory approval and to have completed the acquisition. We now look forward to publishing the titles, which we have admired as competitors for many years. They are a very welcome addition to our French portfolio."
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .