There is a lineage with source on Thomas Lawrence's profile that indicates his lineage to Charlemagne. I included the Richardson source in the Comments on that profile around 2019. I became aware of this linage when I worked on my ancestor Marie/Mary (Lawrence) Burnham, who is a daughter of Thomas Lawrence and Joan Antrobus. For many years, Mary/Marie was mistakenly listed as a 'Tuttle' as Joan Atrobus married 2) John Tuttle. I spent a great while working out and separating this Lawrence/Tuttle lineage, then found the TAG article that Joe referred to and purchased the Roberts Royal Descents of 900 Immigrants published in Baltimore by the Genealogical Publishing Company in 2018 when I was at the NEHGS that year.
There is no point in having a sticker as pointed out by others due to the genetic distance, but one can always point to their several times great grandfather, Thomas Lawrence as having a proven line of descent from Charlemagne.
I became even more familiar with this line, separate from Marie (Lawrence) Burnham being my 8th GGM, when I found that her brother, Thomas Lawrence-952 required a much-needed biography overhaul and to connect his children properly. Chase and Joe helped a great deal with reviewing sources for his daughters. Why was this important? His daughter Mary, married a Thomas Walton. This line was obfuscated with an incorrect Waldren line. It had to be revised and properly sourced for Walton because one of Thomas Lawrence's descendants through his daughter Mary (Lawrence) Walton is Franklin Delano Roosevelt. This line is also pointed out in TAG and in Robert's more recent work in 2018. You won't find a Charlemagne sticker on FDRs profile.
So, only bragging rights to friends and family, but more importantly that it is a 'proven' line, just as we like to do for PGM, MCBs, etc.
And Joe is correct. Roughly half of the males who came over on the boats from Wester Europe are likely descended in some way to Charlemagna.