The three dates will come after their previously-announced gigs in the UK in October.
They will perform at the Bercy Arena, Paris on October 11-12, followed by a gig in Strasbourg at the Zenith Arena on October 16.
Tickets for the shows will go on sale on Monday, March 19.
Radiohead are currently touring the US and Europe until July, including the Coachella Festival, Portugal's Optimus Alive, the Bilbao BBK festival in Spain and Bonnaroo in Tennessee. They will then head to Japan to take part in the Fuji Rock Festival in July.
They will also embark on their first Australian tour in eight years in November.
> Radiohead add more dates to world tour
Listen to Radiohead's 'The Daily Mail' below: