Did Jack not come from the French version of john 'Jaques'?
This is a centuries' old scholarly debate, the short answer of which is most likely no.
First off a correction - Jacques is actually the French form of James, not John (which is Jean).
There appears to have been some discussion in the 19th century as to whether Jack may have originated as a nickname for James and only became associated with John later on (much as Hank originated as a nickname for John before it became associated with Henry) - but later research seems to discount this theory.
The seminal work on this subject is a paper/booklet titled The Pedigree of 'Jack' and of Various Allied Names written by English librarian E. W. B. Nicholson in 1892.
In his research Nicholson found "no recorded instance of Jack, Jak, Jacke or Jakke ever being used to represent Jacques or James".
That being said - names don't develop in a vacuum, nor in laboratory conditions. It's entirely possible that Medieval Englishmen being exposed to the name Jacques influenced the shortening of Jackin to Jack - but short of a time machine trip to ask someone why they chose to go by Jack and not Jackin, it's kind of impossible to prove one way or another.
