The precious egg, made in the style of the famous Fabergé pieces, was discovered on Thursday in a "suspect" BMW pulled over during a routine roadblock near the Swiss border, driven by two Belarusian men who were promptly arrested.
A third Belarusian, a Swiss resident trailing in a Jaguar, was pulled over and arrested a short while later, according to a police statement.
Under questioning, the three men unconvincingly claimed they had found the jewelled work of art lying on the ground, or had bought it cheaply in a flea-market, a French police official told AFP on condition of anonymity.
"They're not talking much," the official said.
"We have the impression we're dealing with a team tasked with transporting and negotiating the sale of the artwork."
The three, aged between 24 and 38, were charged with receiving stolen goods and possessing a weapon.
They were already sought in France and Switzerland for several burglaries.
The egg, containing more than a kilogramme of gold and boasting hundreds of gems, was burgled in 2009 from a Kuwait import-export firm based in Geneva.