The sword, which belonged to eight of the emperor's descendants, was believed to be the last of Napoleon's blades in private hands.
The intricately decorated blade is just under 100cm (40in) in length and has a distinctive gentle curve.
Egyptian inspired design
The sword, which had only been expected to achieve some 1.2m euros was sold in the town of Fontainebleau, near a castle Napoleon used as a retreat.
"It's a world record for a souvenir of the emperor, for a sword and for a weapon in general," auction house spokesman Bernard Croissy said.
The inspiration for the sword's design is said to have come during Napoleon's Egyptian campaign.
He noticed that the swords used by the Arabs, which were also curved, were very effective in cutting off the heads of their French enemies.
The French general is said to have carried the sword into battle at Marengo in June 1800 - before he became emperor - when he launched a surprise attack to push the Austrian army out of Italy and seal a victory for France.
After the battle, Napoleon gave the sword to his brother as a wedding gift and it was then passed down the family through the generations.The sword was declared a national treasure in 1978 and, while it may be sold to a foreign buyer, they must have a French address and keep it in France for six months a year.