The 34-year-old crashed during a 'recon' of the Criterium's fourth stage time trial, ruling him out of competing in this year's Tour de France.
Team Ineos doctor Richard Usher said in a statement: "Chris was taken to Roanne Hospital where initial examinations confirmed multiple injuries, most notably a fractured right femur and right elbow.
"He has also suffered fractured ribs.
"He is now being airlifted to St Etienne University Hospital for further treatment."
Team Principal Dave Brailsford stated the priority now was to ensure "Chris gets the very best possible care, which he will do, so he can recover as soon as possible."
Brailsford said that the four-time Tour de France winner had worked "incredibly hard to get in fantastic shape and was on track for the Tour, which unfortunately he will now miss".
He added: "Even though we all recognise the risks involved in our sport, it's always traumatic when a rider crashes and sustains serious injuries.
"One of the things which sets Chris apart is his mental strength and resilience – and we will support him totally in his recovery, help him to recalibrate and assist him in pursuing his future goals and ambitions."