I'd like to point out that it wasn't Marie Antoinette's necklace, it was commissioned by Louis XV for Madame du Barry. When Louis died, the jewelers tried to sell it to Marie Antoinette, who refused it - either because she thought it was a waste of money, or because she hated Madame du Barry and didn't want her jewelery.

As for the fate of the necklace, Madame de la Motte, the con woman who got Cardinal de Rohan to "buy" the necklace on behalf of a fake Marie Antoinette, removed the diamonds and gave them to her husband, who sold them in London. The location of the specific diamonds is unknown, as diamond sales were not tightly regulated.