Well.. despite the near certainty of *descent* from Charlemagne, the number of generations makes it highly unlikely you actually have any of his genes, unless you're a direct male line or female line descendant (and we know no one is), and even then it's only a tiny fraction of your gene pool. Because of the way zygotes form, you will pass a random mix of your mother's and your father's genes on to your kids. The further back you go, the less chance of any genes from a particular ancestor.
Which is a good thing. You really don't want the Hapsburg result.
Oversimplified a bit no offense. Thing is, we are all the results of genetic inheritance with mutations (which yes is even more of an oversimplification). Now considering we share a high 90s percentage of DNA with most species. Chimpanzees have their DNA on average 1,2% different than ours. considering the number of nucleotides though it leaves a huge amount of variation left.
However let's skip the mitochondrial DNA (which was not mentioned or alluded to in the latter paragraph but would still be important) thing and go let's talk about Xs and Ys, if you will. leaving the almost certain mutation factor, which is still quite small in comparison in each, you will still carry some characteristics of you forefathers, thousands of years removed. they may be common, or not, but they'll be there, mixed in even if the rest got mutated or substitute by the hundreds of ancestor you had between those characters. Sometimes, the it will be simply a protein sequence that gives you crooked little toes, or nothing. but still there and that's in the singular pair of chromosomes I mentioned we could get complicated and go Recessive and dominant alleles. True, You can be a descendent (if far enough removed) and have no genetic similarity and it does increase with time. Soon enough Homo sapiens will be to our future selves what Homus erectus is to us. Soon, I mean in the hundreds of thousands of years. There's a recent study that suggests that over 20% of the population worldwide carries Y characteristics traced back to figures from the mid 9th century. Most East asian, Central nomadic asian, and middle eastern (west asia).
Now by no mean I'll say that everyone descends from them, I mean I just made a joke there in my post. Certainly the majority of people will be in any way related to either (specially in Sub Saharan Africa, which has the most genetic variation, due to a longer isolation from the early migrant populations that went north from our Eastern africa origins. But genetic drift is not quite as probable as you seemed (sorry if I misunderstood) to suggest, in that time span.
It also doesn't mean that just a minority will have one of those ancestries. And I definitely won't mean that the majority will. But a statistically relevant percentage will. You can have his genes from their brother, sisters, parents grandparents, etc. indirectly. I won't be HIS genes, but in that way Only HE has his Genes. His sons, had a part of them.
Thank the Lord for no Habsburgs lips and the myriad of other problems.
Point is sorry I went off topic, on both occasions, specially in this post. I'm bad at jokes.
Cheers,
Dan