Fixing the spear would certainly earn Jon an approving look! Rémi would not praise him directly, but he'd perhaps be a bit less prickly than he has been with some of the others.

Jon may find someone among the Security team willing to help him craft a bow (they've had to learn the hard way, and they can largely acknowledge that sharing knowledge is how they stay alive) however, and you are free as a player to invent this NPC and their relationship to Jon for this purpose!

Rémi will take note of Jon's quiet competence and skill for the future, and depending on what you do with this bow-craft-helping NPC he may be more willing to listen to him in the future based on the opinion of one of his officers, but for the time being Rémi does not seem terribly interested in engaging him further.