Emergency calls in both Europe and the US operate on the same cellular network. And pretty much all of the world that has cell service. Emergency numbers like 112 or 911 just get prioritization in the event of overloading/poor signal/etc.
In Europe, though, AML would send a GPS signal out which would alert emergency services of your failed attempt to call and your location. Not exactly a phone network, but I guess a “separate network” if we’re being technical.