My ggg grandfather John ADAMS (1784-1825) was born in Culpeper, Viginia, and died in Owen, Kentucky, leaving his widow (Sarah HOLTZCLAW Adams) with eight children. I believe (but have not documented) that John ADAMS was the son of Absalom ADAMS Jr (~1758-1823) and the grandson of Absalom Adams Sr (1725-~1810) of Fauquier County, Virginia.
Based on the foregoing, William French "Devil Bill" ADAMS would be my 1st cousin 5x removed. And, the relationship with the presidents Adams was also lore in my family.
Based on my Y-DNA test, I have been assigned to the Adams Surname Y-DNA table as a member of Family 23 [A241]. As I understand Y-DNA data, no one in Family 23 can be paternally related (in genealogical time) to the presidents Adams. There is simply two much difference in the data.