Paco is a Spanish nickname for Francisco. Another nickname for Francisco is Pancho.
The nickname has its origins in Saint Francis of Assisi, who was the father of the Franciscan order. His name was written by the order as Pater Comunitatis (Father of the community); "Paco" is obtained by taking the first syllable of each word.
Sometimes people with the name Francisco are also called Kiko. However, this nickname is more commonly used for Federico, Ricardo, or Enrique.