What you say is true, but I'd add that Gendarms/Guardia Civil/Carabinieri etc.; tend to hang around carrying big guns, are responsible to the country as a whole (rather than the local community), are under the relevant defence ministry (while also reporting to the interior ministry).
In my experience they don't act at all like normal cops, and sometimes can be in conflict with them. The only interactions I ever hear of with citizens is if they beat the shit out of someone. You're not going to be going to them for a lost phone or a cat in a tree.
I don't know about the other forces mentioned here, but the French Gendarmerie are pretty much "regular police" as far as the people are concerned. The main difference with "actual regular police" is that they tend to operate in sparsely populated areas instead of large cities.
But they absolutely will do traffic police on highways, intervene to reason with a loud neighbor, etc. They'll also routinely show up during large protests in big cities.
The "big-gun carrying" Gendarmerie is a special unit, the GIGN, probably akin to US' SWAT teams. They'll intervene when "very dangerous" people are involved, think hostage situations or the like. "Regular police" also has a similar outfit.
Thank you for the correction. Indeed the main force of the French Gendarmerie (Gendarmerie Départementale) is much more like a "regular" police force than I described.
The unit I was confusing with the Gendarmerie as a whole was the Mobile Gendarmerie, whose role is more similar to the the Guardia Civil and Carabinieri.
I wouldn't have included GIGN, since I they appear to be much smaller and have a more "special”/"tactical" role.
I'll also note that the the Gendarmerie don't appear to be sending a team to the AWC (the olympics of smashing through the ceiling and shooting you in your bed) in two weeks, whereas the Guardia Civil and Carabinieri will. This may be a geopolitical thing though.
Seeing Gens D'Armes on the street was somewhat common. The Gens D'Armes are akin to 'heavy' police and are a show of force. The Gens D'Armes were pretty common to see in the subways, airports, and/or just on patrol. They were Gens D'Armes stations in the city just how there were also regular police stations. Gens D'Armes patrols were a bit distinct from other police patrols, almost always larger groups, around 5 to 7 people with long-guns and plate carriers. Meanwhile regular police had much lighter weapons, no body armor, and very rarely were in groups of more than 2 or 3.
Times have changed. Nowadays, the gendarmes only show up when protests are expected to turn into rioting (so basically most of them). You don't see them around Paris in day to day life. We now have actual military patrolling the streets, "Operation Sentinelle". They're supposed to show some muscle to discourage terrorism. They are actual military, with actual military weapons. This has been going on for multiple years, I don't remember when it started.
However, regular police now wear bulletproof vests, too, even when randomly patrolling the streets. Since some years ago, we now have "municipal police", basically police which answer to the mayor [0], as opposed to the state, with somewhat fewer powers. But even they walk around with bullet-proof vests.
---
[0] In France, "the police" usually means "Police Nationale", which answers to the Prefect, who represents the State in the local Jurisdiction (département) – they are not elected, but appointed by the Interior Ministry. The "Municial police" answers to the City, but they're not allowed to conduct all the operations that the National Police do. The City means the Mayor, who's elected by the local population.
> The Gens D'Armes are akin to 'heavy' police and are a show of force
I've only seen that when they show up as support for or operating in a similar role as CRS† (crowd control, security for major events) which indeed would be Gendarmerie Mobile but that's a far cry from the range of operational responsibilities of Gendarmerie as a whole.
Turns out this is probably what city dwellers in France would only see of Gendarmerie, because Police Nationale and Municipale (city) typically have much more presence in cities than countryside, and the other way around for Gendarmerie.
In my experience they don't act at all like normal cops, and sometimes can be in conflict with them. The only interactions I ever hear of with citizens is if they beat the shit out of someone. You're not going to be going to them for a lost phone or a cat in a tree.