It seems although she has worked for Maxwell for many years and interacts with his children daily she can never remember their names this is another running gag of the series. She and Maxwell work in the Sheffield Mansion most days in Maxwell’s office. Maxwell’s office is always very busy with the family and help parading in and out with their day-to-day problems. 
Fran’s parents are Morty and Sylvia Fine. Morty is never shown on camera until the last season and is portrayed by Steve Lawrence of “Steve and Edie” fame. Sylvia is an overweight Jewish mother from Queens. She is constantly eating (another running gag) and isn’t very well educated. While not a stupid woman, she occasionally gets in trouble because of her lack of education. She continually pushes Fran to marry and forces herself onto the Sheffield family and into many of their affairs. The children come to see her as a grandmother figure long before Maxwell and Fran become a couple. 
Fran’s grandmother and Sylvia’s mother is a regular cast member. Her name is Yedda Rosenberg and she is portrayed by Ann Morgan Guilbert (Millie of the Dick Van Dyke Show). Yedda is a chain smoking elderly woman who lives in a retirement home within walking distance of the Sheffield’s home. She left Romania to come to America as a young woman, although she has no accent and speaks perfect English. In the beginning of the series she is portrayed as a widow who occasionally dates but toward the end of the series she marries her African American boyfriend “Sammy” (Ray Charles). Yedda is sometimes very forgetful but at other times very perceptive and wise. The Children love her and so does the rest of the cast. One oddity is however, sometimes when Yedda or Sylvia refer to themselves collectively as a group they will make statements like “We Fine Women” which doesn’t make since as Sylvia married a Fine and Yedda was her mother. 
The other regulars in the cast are Maxwell’s Children: Margaret (Maggie), Brighton (“B”) and Gracie. Maggie in the beginning is portrayed as a very “plain” girl who is shy and unaware of her beauty. Brighton initially is portrayed as mean spirited selfish boy who picks on his sisters and his nannies. Gracie is a troubled little girl (in a comedic way) who is obsessed with her psychotherapy sessions. Fran eventually helps the children grow and become a happy normal family with her “Queen’s Logic” and love for them. Anytime someone has a problem in the Sheffield household Fran has a relative that went through a similar situation, yet another running gag of the show. Often the viewer is led to believe Fran is making up these wild tales but throughout the series her stories prove to be factual.  
Though the storylines in “The Nanny” follow a similar “setup” as “I Love Lucy”, “The Nanny” is much racier and over-the-top than “Lucy.”