Wasn't a medic, but was Airborne, and a Jumpmaster.
Once on the ground, it's just another injury, treat the same as any other. (tl;dr summary)
Before the jump, make sure they're properly trained. You're not a Jumpmaster, or otherwise in the Chain of Command so little to nothing to be done directly about that, other than try to pay attention, some damn fool Colonel who hasn't jumped in a year or more may have pencil whipped his BAR and will be jumping...shockingly that's the guy you need to pay attention to being hurt more so than the scared Pvt on their first jump out of Jump School...
Inside the aircraft, just like on the range, there's Safety, but everyone is a safety officer too, see something dangerous, f***ing say something...much less paperwork later lol
While in the air you obviously can't do jack and sh** about it till they're on the ground, where you treat them no different than if they were in a traffic collision, or fell from a ladder or whatever. Basic trauma protocol. The only thing different/special I can think of would be to pop their canopy release assemblies if not done already, just to prevent an errant gust of wind from catching and dragging your casualty away from you. Otherwise, it's all basic blunt force impact trauma care.
Same BSI/scene safety (don't forget overhead...don't want the second pass dropping something heavy on your head), PENMAN size up, general impression, Level of Consciousness/Alert & Orientation Level, Chief Complaint, (your protocols will probably call for Spinal Motion Restriction/C-Spine precautions), ABC's (though I believe Military is now MARCH - Massive Hemorrhage, Airway, Respirations, Circulation, Head Injury/Hypothermia, basically the same, just spelling out don't forget to tie off arterial bleeds first), Secondary Assessment (this'll be a full head to toe...just please don't be cutting through expensive parachute harness if all they got is an ankle fx and are awake talking to you....that step can probably wait till they're in whatever FLA/MEDEVAC/CASEVAC vehicle you've got...a few jumps I was on in the Reserves we had AMR on standby with an ALS Ambulance, much better than some old HMMWV lol...anyways) and so on and so forth.
As always, consult your local units treatment protocols for trauma injuries, that'll trump anything I (or anyone else) say here. But you already knew that...