"Train approaching"

Solution 1:

Either way this is just a fragment, so the question is what is the rest of the sentence? Your suggestions read as follows, to me:

The train is approaching

A train approaches

I usually interpret it as the following:

There is a train approaching

There's clearly a lot of flexibility when you're only seeing a fragment of the sentence.

Solution 2:

Yes, it's "correct". It is there to carry information, from the metro system to you, namely, that there is a train approaching. And that you should step back ;-)

In all this "proper grammar" and whatever, we (me included, see my rant-with-a-lot-of-comments ;-)) tend to forget that language serves a purpose, to wit, to carry information from A to B (where A to B are very often, but not always, individuals). And as long as it manages this task, to the satifsaction of, well, A and B, all's well.

In this case, I don't see any "failure to inform". So there, job well done, language! Good language, yes, good language! pats language on, uhm, head?