Military police in English-speaking countries usually only have jurisdiction over military installations and military personnel; they do not perform civilian policing functions except in exceptional situations such as wartime or national emergencies. By contrast, gendarmerie are military police who perform civilian policing functions in normal circumstances.
There isn't necessarily a huge difference in practice between gendarmeries and ordinary civilian police forces; gendarmeries tend to have tougher recruitment standards, a more disciplined ethos, be more heavily armed, their members will have received military basic training which covers skill areas which most civilian police training does not, etc. However, even in countries with gendarmeries, the civilian police often have elite units which are on par with those of the gendarmerie; and, in France, much of the gendarmerie are assigned to policing small towns and rural areas which is often less challenging work than that of the civilian police in the big cities.
I confirm in France. I've seen group of policemen (or army?) in the (very crowded) Paris subway stations with dogs and "uzi" weapons.
In Italy there is a civil police force and a military one (named Carabinieri) and both of them carry guns. However, only when they have to raid the homes of high-risk people, e.g. mafia criminals or terrorists, SWAT-like units (named NOCS the police unit and GIS the Carabinieri unit) are deployed.
But yes, machine guns and rifles are only carried by units on special duties, normally anti-terrorism (and unfortunately Italy has a long history of internal terrorism).
In nearly 30 years of living in the US I can only ever recall seeing police officers patrolling with long guns twice: once when I visited the US capitol, and once at a big festival/parade thing in Bellevue, WA.
Seeing the officer in Bellevue patrolling with a long gun was actually quite unsettling. Even though all police in the US are armed and most have a long gun in their vehicle, they very rarely carry them in public. Even at sporting events, airports, etc.
Conversely, during the short period of time I spent in Germany and Austria I saw many police with long guns. (And that echoes my wife’s experiences in France and a couple other European countries.) They were primarily at airports and city centers, so it’s probably a terrorist thing. But it was very apparent—sort of how I imagine Brits feel when they visit a country with regularly armed police.
Rest assured that the small town cops in Europe don’t patrol with MP5s, but that the marines at local US embassy (which is a high value target) occasionally do…
(And the only capitol I visited in Europe was Austria.)
> Rest assured that the small town cops in Europe don’t patrol with MP5s
I understand this. And it wasn't part of my post :)