Francis Floyd did have a daughter named Elizabeth, but she married William Briggs and moved to Illinois. (No marriage record)
1850 Township 2 S R 4 W, Brown Co, IL William Briggs 73 b NC Elizabeth Briggs 74 b VA
in the household just before them:
John Floyd 35 b NC Elizabeth 32 b NCb before the Briggs left NC Mary 14 b IL Rachel 13 b IL William 11 b IL Richard 9 David 6 Jane 5 Jeremiah 2 Daniel 1/12
Elizabeth Briggs married John Floyd Jan 28, 1835 Schuyler Co, IL.
It's my guess that this John Floyd is a son of Francis's son John Floyd, Francis's only son. If so, this was a first cousin marriage, not unheard of at this time.
Francis Floyd's other daughters were Mary Floyd who married Jonathan Elston, March 26, 1800 Rowan Co Margaret Floyd who married Frederick Knup, June 17, 1801 Rowan Co Mimeth Floyd who married William Thompson, March 9, 1811 Rowan Co
This accounts for all of Francis Floyd's daughters - except Nancy who apparently had had not married when Francis wrote his will in 1816. Nancy was the only daughter he actually named. He named the husbands of his married daughters instead.
Rowan Co will book G p 447 Francis Floyd Apr 30, 1816 probated 1816 Son John land adj Samuel Cock & John Briggs. Jonathan Elston. William Briggs, William Thompson, dau Nancy. Son-in-law Andrew Knup. Exr William Bean. Wit Philip Carn, John Moss.
For this reason I believe Whitlock Bean must have married Nancy Floyd as his first wife after 1816 but before the 1820 deed in which Whitlock Bean signed as an heir of Francis Floyd - then married Elizabeth ?? later. I was hoping someone had some records to help determine when the Floyd wife died. Without additional records, there's no way to determine who the mother of his children was.