In my usage:
"Truth" is a potential property of ideas, and only ideas. An idea is true to the degree that it corresponds with (accurately accounts for) the reality which it purports to represent.
So: "This coin is circular" is pretty much true - not entirely, though, as no coin can be perfectly circular.
So: "This politician is a liar" is also liable to be pretty much true, in general - though most politicians tell the truth sometimes.
So: "Every massive body attracts every other massive body with a force that is inversely proportional to the square of the distance between their centres" is excellent as an approximation under most common circumstances in the local universe and for decades was accounted as being true without qualification; but in fact, it is false when bodies get very large or very close.
So: "Stephen is French" is false - though I may have a few "French genes" for all I know, and I speak a modicum of the language.
All of the above statements "exist" and have reality (as statements) so it is possible for "falsity" to exists and "be real" - as a true property of a false statement, which is the most that it ever could be!
Hence "reality" =/= "truth", as some of "reality" consists of "falsehood".
"Is it possible to attain truth?"
This is the crucial question, and it depends on a deeper one: "If one had a true idea, would it be possible to recognise it as being true?" The point is that it isn't much good "accidentally hitting on the truth" if one can't definitely notice the fact that one has done so.
At the deepest level, I think this cannot be answered by logic or reason. These all rely in turn on the assumption that other ideas are themselves true - when this has not yet been established.
I believe that it may be possible to "recognise" that some ideas are true - that some ideas have "the ring of truth" to them. Plato believed that this was because we all have an instinct for truth, based on a direct access to knowledge and understanding of reality which we possessed before and apart from our mortal existence. I don't go along with the specifics of his theory; but I think that something similar must be true, or else one has a real "bootstrapping" problem in epistemology.