John Fitzgerald was until Dial M for Mother the presumed father of Archer, until it transpired that his real father was unknown. Malory concocted the story of Archer's father to protect him from the truth, as she admitted in the aforementioned episode. The backstory given by Malory Archer was he was a Navy Cross-winning fighter ace pilot, nicknamed "Black Jack Archer", who died when Archer was little.
The name is an obvious reference to John Fitzgerald Kennedy, with the scene of Archer saluting at the funeral while standing next to his mother giving it away (it is a famous image of John F. Kennedy, Jr. from his father's funeral at 3). In reality she had paid a Junior ROTC team in Yonkers $600 to give the 21 gun salute, which they used to travel to a competition in Albany and win third place. Like Archer's fictional father, Kennedy was in the Navy during WWII and had a distinguished career, receiving many medals, although not the Navy Cross. He served on a torpedo boat rather than being a pilot.