It does differ from country to country. For example, in France (As I'm sure you are aware), if a person fails to render assistance to a person in danger then they can by held liable. This falls under the "duty to rescue" concept.
Here in the United States (and elsewhere), this is covered by something called the "Good Samaritan Law", which is intended to remove the fear of litigation preventing someone from aiding another in times of distress.
However, it is not a blanket immunity from someone suing. One of the concepts that I was taught when I was a first responder and ER medic in the Armed Forces, is that you are pretty much safe if you act in a manner consistent with either your own training or the training of the general person on the street.
While it is not a guarantee, if you stick within the scope of your training and provide assistance, then you should pretty much be protected. You may still be sued, as there is no bar against a lawsuit being brought, but the Samaritan concept should protect you.
Note, this is not something that covers everything. For example, I was trained and certified in starting IV fluids. US protocol, however, provides that this can only be done when there is contact with a medical control available, and transport to a facility. If I came upon a hiking accident and whipped out an IV, I could still be held liable since that is out of protocol, and I would be considered to be acting outside the scope of common practice.
If you are traveling, your best bet is to look up the laws of emergency responders in the country you are going to. In some countries if it becomes known that you have the certification and you passed by an accident, you can then be held liable and possibly removed from certification because you failed in your duty to act.