His lawyer immediately announced a decision to appeal, which blocks the procedure.
Mukhtar Ablyazov fled Kazakhstan amid the nationalization of BTA Bank, which he once led as chairman. He was arrested in southern France in July 2013 and both Russia and Ukraine have requested his extradition. France has no extradition agreement with Kazakhstan.
Ablyazov's lawyers say the cases against him are political and that he will be sent back to autocratic Kazakhstan if extradited.
A lower French court had ruled to send him back to either Russia or Ukraine in January. The appeals court in Lyon confirmed the decision on Friday.
BTA Bank, one of Kazakhstan's largest financial institutions, welcomed the Lyon court ruling, calling it "an important decision that will allow the bank to continue its efforts to get its billions back."
Lawyers for Ablyazov said Friday they were "confident" that Lyon court rulings "will be overturned at one of the multiple, subsequent levels of appeal."
Friday's hearing in Lyon was the latest episode in a saga that began in 2001, when Ablyazov, once a trusted member of Kazakh leader Nursultan Nazarbayev's inner circle, turned against his mentor and founded an opposition movement. The oligarch-turned-dissident fled Kazakhstan in 2009.
In Britain, where Ablyazov received political asylum in 2011, courts found he concealed assets as BTA sought to recover more than $6 billion the bank says he appropriated.
Ablyazov fled Britain in 2012 and had been on the run for 18 months under international warrant until his arrest in southern France, where he is jailed.