We only hear of three d'Anconias in the book: Francisco's father and his two famous ancestors Sebastián d'Anconia and his wife. Francisco's father has a lot in common with the Taggarts. He seems like a good man, and Francisco is quite loyal to him. However, even though he is proud of his son, Francisco's father seems rather confused by Francisco's ability and ambition. There's something of a disconnect between father and son, similar to Dagny's disconnect with her mother. Francisco's father died when he was quite young; this helped precipitate Francisco's disillusionment with the world and led him to join Galt's crusade a few years later.
Analogy time: Francisco is to his famous ancestors as Dagny is to Nat Taggart. In other words, Sebastián d'Anconia and his wife inspire Francisco in his life's work. And Sebastián's rather epic love story also serves as a template for the hopes that Francisco harbors for his relationship with Dagny.