When you get confused by the notes, stop looking. Listen. If you forget the chords and listen and understand how the harmonic tension is working, I think you'll agree the passage overall doesn't feel like it comes to a conclusion, like a full cadence. But there is a sense of tension and then relaxation. To me it sounds like a half cadence with an unusual flavor of Phrygian motion. There is a long tradition of monkeying around with the inner notes in Phrygian cadences, the most notable version being the French, Italian, and German augmented 6th chords, all of which serve the same (pre-dominant) function.
With these thoughts on the functions of the chords, let's look at the notes. If this is a Phrygian sort of motion, then the passage is in the key of A minor, with F chord acting as a chromaticized VI and the E chord being a v. To confirm this, I sat down at a piano and played the passage and inserted an A minor chord at the end, to see if it "sounds right." I think it does.
The F chord is a little odd because it contains an Ab, making the chord minor. You'd think this would make it sound pretty weird, and it does have a spooky sound to it, but it still works because Ab is enharmonic with G#, and G# is in the scale for A minor (harmonic or melodic). So adding the Ab does not take it out of key.
Also, the E chord is unusual in that it is dominant function but minor. This is what gives the passage a sort of sad and uncertain release.
And finally, there is a false relation between the A natural in the melody and the A flat in the harmony, which heightens the tension and mystery of the first chord.
If I had to write this in Roman numeral notation, it'd be either
bvi v (traditional notation)
vib3 v (Aldwell & Schacter)
vi* v (pragmatic shorthand that expresses the function)
P.S. I love this passage; it's one of my favorite leitmotifs in the film. Reminds me a little of the overture to Tristan and Isolde, and is even in the same key, coincidentally.
P.P.S. Maybe you noticed but this arrangement contains parallel fifths. Rules are meant to be broken, yo.