I don't want to know the emergency number in case I'm IN a different country. What I want to know is, if I am, say, in France, and I know someone in Sweden needs emergent services, how can I call, from France, the emergency services in Sweden? Forgive me if that sounds confusing, but I'm surprised nobody has asked this question, even if it may be stupid. I'm wondering if I can call help for someone in a different country, if I know they need help and am the only one able to call, maybe by adding a country code. Would that work?
Commonly, emergency phone numbers like 911 in the US or 112 in most European countries can not be called from abroad. Even within the country, emergency calls are usually handled completely different in the phone network, allowing the calls to be connected with priority, routed to the closest dispatcher centre and passing on details about the caller like e.g. the address of a land line or the approximate location of a cell phone.
That does of course not mean that emergency services like police, fire departments or ambulance services can't be called from abroad, you just have to use their regular phone numbers. For example, the emergency number in Sweden is 112 and can be dialled from within Sweden and should only be used for imminent emergencies. The regular (non-emergency) phone number for the police is 11414 and will connect you with the closest police station. When calling from abroad, you can reach the Swedish police under the number +46 77 1141400.
Most countries can pass calls between them. The European Emergency Number association produces a database that is available to bone fide emergency control rooms. So call your local emergency number and see what they can do.