Russian authorities opened proceedings against Vitaly Arkhangelsky, 36, head of Oslo Marine Group (OMG), a sea transport and port operations firm, after he was accused of contracting huge debts with several Russian banks including the Bank St Petersburg.
He fled with his family to Nice in the south of France four years ago and in turn accused the Saint Peterburg bank of embezzling his funds.
In its ruling, the Aix-en-Provence appeals court said "serious doubts" existed concerning the fairness of the proceedings undertaken against Arkhangelsky.
It said extradition would expose him to the risk of inhumane and degrading treatment and would represent a disproportionate attack on his right to a private and family life.
Arkhangelsky's firm, OMG, once valued at a billion dollars (746 million euros), is now worth barely one fifth of that and most of its subsidiaries have gone bust, according to his lawyer Francois Ameli.
"The bank has taken all his assets," he said, estimating the bank's illegal take at "300 million dollars."
Arkhangelsky filed a civil case against Bank St Petersburg in Nice in January, accusing the bank of fraud and using false documents.