Prénoms composés are a single first name, not a first and middle name as foreigners often believe.
I find it very annoying when called “Jean” while my first name is “Jean-Louis”.
French people do not use nicknames that much, and at least much less than Americans and in any case, it is almost never the first name of a compound one, especially when it is “Jean” which used to be very common case.
It is just like you don't refer to “San Francisco” as “San” or “New-York” as “New”.
It might be the last one though. I know people named "Pierre-Cyril" and "Marie-Ghislaine" who used to be called "Cyril" and "Ghislaine".
In any case, don't try to guess a nickname from someone's first name, there is no generic rule. Never use a nickname unless you know that other people already doingdo it.