Francis was the son of William Pym and Elizabeth née Kingsley and lived at the family seat of Hasells Hall (which he considerably improved) in Sandy, Bedfordshire.
He married Anne Palmer in 1784; they had four sons: Francis, Revd William Wollaston, Robert and Charles and two daughters Anne and Catherine who all survived them, and two sons who did not, one having died in infancy and the other, John, a lieutenant in the 13th Light Dragoons, having been killed at the Battle of Waterloo.
He is buried in Sandy, Bedfordshire with a monument sculpted by Thomas Denman.
It is a Grade II listed manor house, with grounds designed by Humphry Repton.
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