"[Jack], the commonest pet-name for John, has caused a good deal of difficulty owing to the natural assumption that it must be derived from the French Jacques and should therefore logically represent James rather than John. The problem was cleared up by E. W. B. Nicholson in a little book entitled The Pedigree of Jack and of Various Allied Names (1892). He showed that there is no recorded instance of Jack, Jak, Jacke, or Jakke ever being used to represent Jacques or James, and that no statement in favor of the French connexion has been produced from any early writer. He then proceeded to elucidate and illustrate with examples the development of Johannes [the standard Latin nominative form] to Jehan [the standard Old and Middle French oblique form] and Jan [the standard Middle Dutch form], whence, by addition of the common suffix -kin [a uniquely English suffix], we get Jankin, which as a result of French nasalization becomes Jackin [this is the same nasalization that gets us Harry from Henry], and was finally shortened to Jack. There was a similar development from Jon to Jock (the Scottish form of the name)."
https://dmnes.wordpress.com/2017/01/28/why-is-jack-a-nicknam...
"[Jack], the commonest pet-name for John, has caused a good deal of difficulty owing to the natural assumption that it must be derived from the French Jacques and should therefore logically represent James rather than John. The problem was cleared up by E. W. B. Nicholson in a little book entitled The Pedigree of Jack and of Various Allied Names (1892). He showed that there is no recorded instance of Jack, Jak, Jacke, or Jakke ever being used to represent Jacques or James, and that no statement in favor of the French connexion has been produced from any early writer. He then proceeded to elucidate and illustrate with examples the development of Johannes [the standard Latin nominative form] to Jehan [the standard Old and Middle French oblique form] and Jan [the standard Middle Dutch form], whence, by addition of the common suffix -kin [a uniquely English suffix], we get Jankin, which as a result of French nasalization becomes Jackin [this is the same nasalization that gets us Harry from Henry], and was finally shortened to Jack. There was a similar development from Jon to Jock (the Scottish form of the name)."