The reason why Fran gets her first question right on Jeopardy is because---at the time---a famous commercial ran on TV for English muffins, depicting the exact trivia, complete with dates, that Fran retells.
The title comes from the sitcom Nanny and the Professor (1970) about another odd nanny-single father family relationship.
C.C. comments on Fran's intelligence, saying she went to Nick at Nite school (meaning she acquired her knowledge from television), which was a night time programming block on Nickelodeon, known for its lineup of syndicated sitcoms. The Nanny was added to the lineup on May 10, 2009 until October 26, 2013.