The Royal Coronation Crown of Charlemagne was real. But, the coronation crown, the Crown of Charlemagne, was destroyed in the French Revolution, like most of the medieval Royal Regalia.
The crown we know as the Crown of Charlemagne was actually fabricated sometime after 1237. Since Charlemagne died in 814 the likelihood of him actually wearing the crown seems small. Apparently, Charles the Bald (I’m not making that name up) had the crown made. Charles was King of the Franks from 840 to 877 and Emperor of the Holy Roman Empire from 875 to 877. Ol’ Chuck was a man of simple tastes (for a king) and the crown was just a circle of four curved rectangular plates with jewels affixed.
In the years after Charles, the fleur-de-lis became the symbol of the monarchy. Historians believe Philip Augustus, A.K.A. Philip II was a fashionable guy and liked a bit of decoration. He probably added four fleur-de-lis to the crown in about 1180.
Philip II was the King of France from 1180 to 1223, and the first to be called by that title. His predecessors had been known as Roi des Francs (King of the Franks). Since the French were all about good food, and no one wanted to be associated with the hot dog, they changed the name. From 1190 onward Philip was known as Roi de France (King of France).
A second crown was fabricated approximately the same time as the first and was used to crown the Queen. Sadly, the French began to fight about which church to attend and one of the crowns was melted during the siege of Paris in 1590. (The siege was part of the Wars of Religion, a two hundred year long mess that historians can’t seem to explain any better than the people of the time could. Suffice it to say that the Protestants lost and hundreds of thousands died.)
The remaining crown was used until the reign of King Louis XVI, who was crowned in 1775 in the Cathedral in Reims. French kings had also their personal crowns, worn after the coronation during a big banquet. This turned out to be a good deal for the church as the crowns were later donated to the treasury of the Abbey of Saint Denis near Paris, the traditional burial place of the Capetian dynasty
The Imperial Crown of the Holy Roman Empire or Reichskrone, probably made for the coronation of Otto the Great in 962 is sometimes called the Crown of Charlemagne. However, it was fabricated several hundred years after Charlemagne.
When Napoleon proclaimed himself Emperor of France, he also called his own imperial crown Crown of Charlemagne. He called it that, but, really, we all know he was nuts.