Paco

[Sancho Panther]

Why is 'Paco' the diminutive of 'Francisco'?

[Rusty]

There are several online sources that give an explanation, but the information given here (http://spanishlinguist.us/2013/03/pepe-and-paco-2-mysterious-spanish-nicknames/) says that the folks at the RAE disagree with that information.
Since the RAE didn't provide an answer to your question, let's see if a native speaker has the answer.

[AngelicaDeAlquezar]

@Sancho: You may find useful this commentary:

http://udep.edu.pe/castellanoactual/me-llamo-francisco-pero-me-dicen-paco/

[JPablo]

Interesting question!

(And interesting theories!!)