Interesting - where in the world is this the case? Mexico? I had a Spanish friend called Francisco, known as Paco, but a Portuguese Francisco I know was utterly baffled that his name could be shortened that way.
That'd be for the Basque Country region, the region of origin for Jai Alai.
There, the equivalent for Francisco is Frantzisko, although I think is way less commonly used. I almost always hear Patxi, even in formal settings. For example, a former President of the Basque Government (the Lehendakari), and also former President of the Spanish Congress of Deputies, always goes by "Patxi" (Patxi Lopez).
Also, like in the Patxi Lopez case, you might be born or living in the Basque Country and named Francisco, but go by Patxi.
Going by Patxi when you're named François it's because the Basque Country region also overlaps with France.
> Paco is a Spanish nickname for Francisco. According to folk etymology, the nickname has its origins in Saint Francis of Assisi, who was the father of the Franciscan order; his name was written in Latin by the order as pater communitatis (father of the community); hence "Paco" was supposedly obtained by taking the first syllable of each word.
https://es.wikipedia.org/wiki/Francisco has the same description, and comments that it's similar to how José is "Pepe" through "P(ater) P(utativus)", the husband of Mary, the father of Jesus. It then adds "[cita requerida]" to that description.
https://spanish.stackexchange.com/questions/17631/why-is-pac... mentions that one, and adds another possibility; writing "Phranciscus (the latinised version of Francisco de Asís's nickname) as Ph.co in signs and inscriptions", thus becoming "Paco", "Pacho", and "Pancho".
I know that when romans invented latin they transliterated greek letter Φ to P. So I checked the name written in greek and sure enough it could be abbreviated as paco if you don't know how to pronounce it : Φραγκίσκος
"Beppe" and the less used "Beppo" are both diminutives (not nicknames) of the popular (especially back in the day) biblical name Giuseppe.
"Chicco" is an interesting case in Italian, as it is more of a nickname than a diminutive (hypocoristic, to be precise), and it can be used for the full names Francesco, Enrico, or Federico.
There, the equivalent for Francisco is Frantzisko, although I think is way less commonly used. I almost always hear Patxi, even in formal settings. For example, a former President of the Basque Government (the Lehendakari), and also former President of the Spanish Congress of Deputies, always goes by "Patxi" (Patxi Lopez).
Also, like in the Patxi Lopez case, you might be born or living in the Basque Country and named Francisco, but go by Patxi.
Going by Patxi when you're named François it's because the Basque Country region also overlaps with France.