It would not. Aircraft have other navigation systems they can use instead, such as inertial reference and ground-based VOR navigation. And where there's radar coverage, they can be vectored by controllers.
This probably couldn't be used to keep up with the volume of air traffic today, but it would be enough to get existing flights down safely.
For landing, ILS is still very common, and doesn't require GPS either. An aircraft planning to land at an airport without ILS will have no trouble finding a nearby diversion airport that does have it.
Even as more ground-based navigation beacons are decommissioned, retaining enough for such an emergency remains an active consideration.
And pilots can land with a visual approach and still have ILS.
You would still have ADSB with your altitude, and I beleive heading and airspeed.
Because of the existing requirement to be spotting traffic and being over 1000ft away from other planes, they should be fine.
ATC should still have radar vectoring for their airspace.
I assume planes use more then just GPS, and use galileo and the other networks like consumer GPS do.
For light aircraft getting lost in the old days one hack used to be to fly low till you came to a motorway and read the signs. I imagine most such pilots these days would pull out their phone and open the maps app. Commercial flights of course have more high tech stuff like radio beacons.