Statistics are impossible to make, but it is very likely that most (if not all) people in North-Western European descend from Charlemagne (and, by him also Clovis).
I started making a
list of families descending from Charlemagne using his official genealogy, but I stopped at the 11th generation (20th for Belgium only).
I can myself trace my ancestry back to Charlemagne via the Dukes of Brabant, but some connections around the 16th century are a bit shaky (documents not always reliable or available).
Anyhow, unless one descends hundreds of times from an ancestor who lived 1200 years ago (so roughly 40-50 generations), the amount of DNA inherited from that ancestor could very well be nil. What's more, even with a proven paper genealogy, there are never any proof that one's maternal ancestors were always faithful, or that secret adoptions didn't take place. That's why I don't give much credit to paper genealogy anymore, especially since DNA tests became so readily available.
I wish that Charlemagne's full genome could be tested one day and compared with the modern European population. I suppose that the highest similarities will be found around the Frankish homeland (Rhineland, Belgium, Luxembourg, northern France). It might be interesting to try to find the individuals with the highest percentage of shared DNA to have a better idea of what Charlemagne looked like. We could already ascertain his hair and eye colour and skin pigmentation from raw DNA. Ultimately I believe it will be possible to reconstitute any historical person's approximative looks based on his or her DNA.