Also playing the summer bash at Henham Park Estate, Suffolk are MIA, The Breeders, Death Cab For Cutie and Amadou & Mariam.
The bill also features an extensive list of comedians including Bill Bailey, Ross Noble, Rich Hall, Simon Amstell, Russell Howard, Phil Jupitus and Lucy Porter.
A literary arena at the festival will have readings from Iain Banks, Irvine Welsh, Mike Gayle, Stuart Maconie and Simon Armitage.
Festival curator Jon Dunn told eFestivals: "I'm excited with our headliners for this year’s festival and looking forward to announcing further great acts over the forthcoming weeks.
"Franz Ferdinand will be phenomenal, Interpol will rock and captivate and the beautifully ethereal and epic Sigur Ros will soar."
The event takes place on July 17-20. Tickets are currently on sale.