The majority of Western Europeans are related to, not descended from, Charlemagne. Crucial difference.
Nope, descended from.
Probably all of Europe and much of the Near East.
His descendants have ruled most of Europe.
Here is how it works.
He had at least 20 known children (Discounting a few rumbles in the hay with some servant prior to his kingship)
Louis the Pious Had 10 Children and 40 Grand Children (ironically there are only 10 other Documented Great Grandchildren of Charlemagne's Line).
This is not totally surprising because only 7 out of his 10 children that were legal survived to adulthood.
They went on to marry into every noble house of Europe quite quickly.
So you have a king, has 3 sons 1 daghter and a bastard.
Daughter gets married off to a count, son 1 gets kingship, Son 2 and 3 become minor nobles. Bastard joins the Army.
Minor nobles have kids, they become knights, Knights have kids who become nobodies.
Etc...
So yes, unless the person in Western Europe's Ancestors were from a non-European Country, then their ancestor was Charlemagne.
Statistically (In reference to Joseph Chang of Yale's Statistics)
The most recent common ancestor of every European today (except for recent immigrants to the Continent) was someone who lived in Europe in the surprisingly recent past—only about 600 years ago. In other words, all Europeans alive today have among their ancestors the same man or woman who lived around 1400. Before that date, according to Chang’s model, the number of ancestors common to all Europeans today increased, until, about a thousand years ago, a peculiar situation prevailed: 20 percent of the adult Europeans alive in 1000 would turn out to be the ancestors of no one living today (that is, they had no children or all their descendants eventually died childless); each of the remaining 80 percent would turn out to be a direct ancestor of every European living today.
From Genetics.
“A genetic survey concludes that all Europeans living today are related to the same set of ancestors who lived 1,000 years ago. And you wouldn’t have to go back much further to find that everyone in the world is related to each other.