I've been doing some digging and found out where the name Francomb came from.
Annis Francomb Drew born 14 April 1854 Yate, (although you have 1851 in your post)
Robert Parker Drew married Elizabeth Ann Cole 29.3.1853 at Old Sodbury.
Elizabeth Ann Cole then died in Jan 1855.
Elizabeth Ann Cole's father was William Cole, and her mother Emma Jane Bendall, married 13 May 1822 Westerleigh.
All the above from a tree on MyHeritage, but with all the dates to support the evidence it would seem fairly reliable.
Coming to it from a different direction, there is a whole section on The National Archives for wills proved at the PCC (Prerogative Court of Canterbury). They are free to download at the moment if you're registered and signed in - all free to do.
There is a will for a Thomas Francomb, 'Gentleman of Old Sodbury'. March 1832.
He would seem to be unmarried, and leaves a couple of messuages for the benefit of his servant Martha Tilling for her lifetime, and then after her decease to James Cole of the Parks farm in Old Sodbury, who is also his executor.
James Cole is married to Thomas Francomb's sister Ann.
Children mentioned as receiving bequests ar Betty, wife of Mr James Holloway of Church Yatton; and Charles and William Cole.
So I think the relationship between Annis and Thomas Francomb goes like this:
Annis Francomb Drew -
mother Elizabeth Ann Cole -
father William Cole -
father James Cole - wife Ann Francomb
brother Thomas Francomb
Ann Francomb was the great grandmother of Annis Francomb Drew.
Perhaps 'Annis' was a pet name of 'Ann'.