Just to support that there's most likely no EU-level law about what you ask, the EU publsihed Practical Handbook for Boder Guards (Schengen Handbook) only mentions weapons once, when it comes to a reason for searching a vehicle, i.e. suspicion of weapons smuggling. It also mentions firearms exactly once, again as being part of items that can be seized. It says nothing about guards pulling or using their firearms/weapons etc. That's mostly left to national laws (and some other agreements, see further below).
The "Study on
on Border Officers
Operating at the
of the EU", which is mostly concerned with guest border guards from other EU states says
A detailed analysis shows very different answers from concerned
States to each practical question regarding the right to wear a
uniform (3 countries ignore or limit this right, on the contrary 9
consider that it is an obligation), to wear a service weapon, to
access private property, request ID or travel documents, access to
information systems, interview persons, check for the correctness of
information, reporting, using force etc. Analysing the 70 possible
tasks related to EU border control, the number of tasks that may be
conferred to guest officers varies - depending on which country is
analysed- between 2 and 60 (!).
These different answers (even when facing identical situations)
demonstrate the current lack of a consistent legal framework in
Europe in order to regulate the conferment of powers during EU
joint operations. It is also the evidence that our common legal basis
(the Schengen “acquis”, our common strategy – even coordinated
by a common agency) is too general to be translated into
operational realities just based on bilateral agreements, and without
making a minimal effort to agree on common basic rules. The
elaboration effort will be facilitated by commonalities in many
existing agreements, regarding cases of self defence, emergency
situations, hot pursuit etc.
I.e. there's vast variation on even the laws/regulations for carrying a service weapon, from which one can entail that that also applied to using it. Actually, the have a giant table with the rights, which include these rows on service weapon: carry, use individual, and use of collective weapon (no idea what that last bit means exactly--crew-served weapons or area weapons). The caption that goes before that giant table is:
Below is a generic table
illustrating the tasks carried out by border control services in the 28
relevant States, consequently combining explicit legal provisions
from the above-mentioned acts and prerogatives implied in the
generic competence of controlling borders.
For completeness sake, fewer of these countries allow a guest border guard (i.e. from another EU country) to carry a weapon... or to bring it with them; only about half the EU countries do that:
and even fewer (11 countries) allow guest border guards to use their weapons.
It's mostly the countries of the Prüm Convention which allow other officers from other EU countries to carry weapons; but there also bilateral agreements between EU states--France and Germany have one also UK has one with France. (The study is from 2006, whereas according to Wikipedia, more countries joined the Prüm convention in subsequent years.) It's worth investigating if the convention unifies the conditions for the right to use a service weapon... but it turns out that it's very general, and mostly it defers to the local/host laws:
(the EU pdf on this is borked to use a private character set, so here's an image instead):
So besides some general principles, there's nothing like a uniformization of service weapons regulations in the EU.
Also, as to whether they are armed, mostly yes, on their home country territory. It gets really complicated with the guest guards.
The cultures of the various law enforcement services show
remarkable differences related to carrying service weapons. These
distinctions are illustrated as follows:
Border control officers do not have the right to carry weapons
in every State (e.g. the UK, Malta). In other countries like
Norway, police officers are usually not armed when operating
in home forces, but carry a weapon when they participate in
According to the Internal Regulations of the National Police,
French officers have the obligation to carry their service
weapon when they wear their uniform. This has been the
subject of discussions with Slovakia for example when it
organised a JO authorising foreign uniforms but not weapons.
So if you really want an answer about the Ceuta case, you should probably ask about he Spanish laws instead.