No one was reported injured in the robbery.
Police said the operation was carried out by one man.
An investigations officer with the Alliance police union, Olivier Lebon, said a man in his 50s and wearing a suit walked into the boutique in the afternoon. He threatened employees with a gun, and, minutes later, walked calmly out of the store with his loot.
It was not immediately known whether he had an accomplice outside the store or waiting elsewhere.
Numerous jewelers, as well as France's Justice Ministry, are located on the elegant Place Vendome which is usually filled Saturday with strollers soaking up the sunshine.
The estimated value of the stolen jewels is far below the euro80 million in watches and jewels stolen from the Harry Winston shop in Paris in December 2008.