Franklin was Jack Harkness's father. He lived on the Boeshane Peninsula with his wife and his two sons, Jack and Gray. He used to play what appeared to be cricket.
During the attack by the "worst creatures in existence," he ordered Jack to flee with Gray (Jack accidentally let go of Gray's hand), and, eventually, Franklin was killed by the creatures. Jack returned home to find his mother cradling Franklin's corpse.
Franklin later appeared to Jack when he was hunting a Weevil in the sewers. The memory-changing alien Adam, masquerading as one of the Torchwood team, made Jack remember his past. Franklin was included in that illusion. (TV: Adam)