The identity of the buyer was not made public but the French government has issued an export ban and classified the guns as national treasures.
Inlaid with gold and silver, the pistols feature an engraved image of Napoleon. They sold at the Osenat auction house in Fontainebleau, south of Paris, on Sunday, exceeding the top catalogue estimate of €1.5m.
The guns are said to have almost been used to end the French ruler's life in 1814, when he was forced to give up power after foreign forces defeated his army and occupied Paris.
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