Parkour doesn't have to work like in TitanFall. It could be a replacement for Jetpack and Sprint, and even Mancannons to an extent. Forge would come with a new Mobility category in the inventory. Some items could be:
Ladder
Wall, Parkour
Billboard, Parkour
Parkour Brush, Natural
Parkour Brush, Artificial
Parkour Brush, Digital
Parkour Toggler
Ladders would work as always.
Walls/billboards would work how we've seen in TitanFall.
A "Parkour Brush" would modify existing objects. Rather than pick up objects with it held, you can "paint" objects over with a flag that would allow them to be used by the Parkour button and change the dimensions of the brush in the process. Natural would cover objects in things like vines, Artificial in handrails and steps, and Digital in more HUD-looking space noise that would indicate you can wallrun on them. You can also use checkboxes to indicate what modes of Parkour they allow: Horizontal, Vertical, or Free Movement. Horizontal would consist of wallrunning, Vertical of Ladder-style climbing, and Free Movement lets them move anywhere it's brushed.
The Parkour Toggler allows you to click an object and pick Horizontal/Vertical/Free Movement. This allows the entire object to be used by the Parkour button, for example making a crate float in midair and covering it in vines.
I also personally wouldn't expect to be able to use your weapon while parkour-ing in Halo, but TitanFall proved me wrong on that one.