The crown on the left is the crown of Louis 15th (XV) of France. We will return to the other.
Each king had his own crown during the ancient regime. The crowns were kept in the basilica of San Denis.
During the French Revolution, crowns were a symbol of oppression instead of a symbol of history. There were 20 crowns before the Revolution, one of which was believed to belong to Charlemagne. After? There is only one, the crown of Louis 15th, here. The rest have been destroyed.
In fact, it's only part of the crown. The crown originally had many diamonds, rubies, emeralds and sapphires. In 1885 the government of the Third Republic, lacking a sense of history, decided to sell the jewelry to earn some easy money. And therefore, what we see here is not jewels but only pieces of glass.
I can't find anything on the other crown on the Louvre website. But if you trust Wikipedia, it's the crown that Napoleon used for his coronation in 1804. It is not impossible, but it is strange that there is nothing on the website about it.