You are just one of 16 million according to the National Geographic, May you should get the cousins together for a reunion,

There are many reputable companies where you can get your DNA tested. Thsi is one.

If you saw that in a subscriber submitted family tree,you need to document it yourself before you claim it. Ancestry.Com is probably the best website for original source records, but family trees on any website, free or one like Ancestry.Com should be verified. Online family trees are not records. They are subscriber submitted, mostly not documented or poorly documented. You frequently will see different info on the same people from different subscribers and then you will see the absolute same info on the same people from different subscribers, but that is no proof it is correct. A lot of people copy without verifying and believe me there are errors in online family trees.
You can submit a fictitious family tree and it will be accepted. If you disagree with something someone has posted on one of your family, the owners of the websites will tell you that is between you and the other subscriber. There is a genealogy on the British Royal Family that takes them back to the Royal Line of David but it is based on jumping to a conclusion. Documentation/records are the meat of genealogy. It doesn't prove they are or they aren't.

Now, putting that aside, a lot of people are no doubt descended from Charlemagne. Some say the law of probability is that almost all Europeans are, but for most they will never find the documentation.

If you get back to your 39xgreat grandparents, that is 42 generations including yourself, if each of those 39 great grandparents was a different person, you would have more than 1 trillion, 162 billion of them.
Many people living today there 39xgreat grandparents would be living in the time of Charlemagne.
See it pyramids as you go back. If you aren't a mathematician sit down on a ruled pad number it one through 39. Start off with your great grandparents, you have 8 of them, then you have 16 great great grandparents, 32 great great great grandparents, 64 great great great great grandparents and so on until you get to 39. You should have a calculator or adding machine handy. For each generation double it from the generation right before it.
The population of the world is estimated to have been only about 30 million at that time. So you see it would be absolutely impossible for each one of your 39xgreat grandparents to each be a different person.
The 30 million, no doubt includes children that never reached adulthood
and had children. Also if you narrow it down to the population of Europe or even Eurasia which I don't know what that figure is but it would definitely be less than the population of the world, the law of probability that you are descended from Charlemagne is even greater.

But if you can get the documentation that you are, no way are you alone.

Edit: I might add your Mitochondrial might indicate you are and might not. but wouldn't prove you aren't. You get your Y from your father. Mitochondrial goes from mother to both sons and daughters but only the daughters pass it on to their children. If you had both done, by the time you get back to your over 1 trillion, 162 billion 39xgreat grandparents, you would have received your Y from only 1 of them and your Mitochondrial from only 1 of them. So no way can you disprove you aren't descended from Charlemagne with either Y or Mitochondrial.