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Father Addams is the deceased father of Gomez Addams, Uncle Fester, Pancho Addams and Cosimo Addams.
He was the husband of Grandmama, therefore making her his widow, but in his only appearance (as a statue), his wife is Mother Addams, since Grandmama was Morticia Addams' mother in that incarnation.
The Addams Family (1991)
Morticia mentions Mother and Father Addams as she walks in the cemetery with Fester. She wishes the children could've known them better: "...tell that to an angry mob."
Appearance
Father Addams died an elderly man, with a slight beard--presumably grey. He wore a top hat and a suit. It is mentioned in one of the incarnations that he started growing hair when he was 50 years old, which would mean that baldness is a trait in the family (and is passed on to Fester).