Not presenting myself as an authoritative expert, but while tinfoil might work, I would cover the hole with something more solid – say a small square of copper taken from roof flashing material – and then cover that with several pieces of metal foil tape (you could also do that on the interior side just to be sure). I'm not sure if the door seal on gun safes (product which is designed to expand with heat and “pressure seal” the door opening is electrically conductive or not (I suspect not as that I've examined has a rubberized outer jacket). I believe it's possible that you'll have to make a choice whether your safe will primarily seal from heat, fire (and potentially water incursion) or primarily shield from EMP energies. I'm thinking that one possible alternative might be to use a metallic thread EMP shielding fabric as a “cover sheet” over the front of the gun safe, having it held in place by magnetic strips around the entire outer perimeter – thus covering the gap between the door and the body of the safe, but still readily allowing for access with a complex repacking requirement. Nice thing about having a combination gun safe/Faraday Cage would be that any electronic optics installed on your guns would be protected from possible EMP damages. I'd add this question to the list for follow up with Andrew for his thoughts/insights.
Added thought – you need to make sure that interior of the safe (especially the thin-wall locker styles) isn't electrically in contact with objects you're protecting (i.e. wood or cardboard linings probably best).