Either that shield should not be able to activate while in mid-air, your character should lose all momentum mid-jump and fall in the stream, or your character should be unable to prepare for his fall due to his muscles seizing up and splat onto his face.
I dropped the IC explanation in favor of churning out the post faster; had already crossed the three day limit by an hour or so at that point.
The aura itself works much differently from conventional armor; or even a physical object, for the matter of fact. It moves together with Gigue's body, yet there is absolutely zero force transfer - the aura does not ever actually touch his skin, hovering just a millimeter above. That is due to the aura being fixed to his own Ki system, instead of the physical body.
The above means that the aura does not interfere with the jump's momentum, as Gigue himself is the carrier, so he wouldn't just plop into the river upon activating it.
Before activating the Hyperarmor, he can put his body in such a position mid-air, that when he lands, he has both his feet on the ground, legs crouching, while his arm is put in front and is preventing him from toppling forwards. All he'd need to do for this is stick his arm out and pull his legs up, the latter already naturally occurring when one jumps.
Frankly, i thought i had that included as his landing position of choice in the previous post - but apparently not. Quite a few things i'm omitting from them, intentional or not. :/
The aura would also absorb the momentum of his jump, putting him at a neutral state once he has landed, so he can start moving almost instantaneously, and as result, there would be almost no difference between a jump with Hyperarmor and without, since in the latter case Gigue would have to dampen the momentum with his own muscle force, which would lead to a slight pause in his actions as well.