Hi Nathan
It was Joseph Chang, a mathematician from Yale, who first theorised that everyone of European extraction must be descended from Charlemagne and also from Mohammed and many other notable figures from that period.
I think it's based on that fact that the mathematical progression of generations (2 parents, 4 grandparents, 8 great grandparents, 16, 32, 64, etc) before too long leads to more people than are thought to have existed on earth in the eighth century. Even taking into account pedigree collapse and other issues.
Any European descent from Mohammed it likely to be via Islamic (Moorish) Spain and the Christian dynasties in Spain and southern France, and Edward I's mother Eleanor of Provence could be a good candidate, but the problem is actually proving such a descent. My understanding is that there is plenty of theories but no such pedigree with absolute proof.
Unfortunately on WikiTree there are still many pre-1500 profiles that have to be checked and as Eva has written, there are problems with the link from Ibn Abu-Musa and Edward I