Völuspá Text, from http://www.voluspa.org/voluspa1-5.htm
Ár var alda þar er Ýmir bygði,
vara sandr né sær né svalar unnir,
jörð fannsk æva né upphiminn,
gap var ginnunga, en gras hvergi.
OK, text again, with alliterating (and assumed stressed) syllables highlighted:
Ár var alda þar er Ýmir bygði,
vara sandr né sær né svalar unnir,
jörð fannsk æva né upphiminn,
gap var ginnunga, en gras hvergi.
The music from the 1780 French book:

Notes that correspond to highlighted syllables:
(F-G) F A
A A G
F F (maybe)
A G G
Notes:
All assignments of stresses are my best guesses, as I don't speak a lick of Icelandic. Will have to ask Deirdre for help.
Line 1: Not really sure if 'Ar' is stressed or not. It looks a lot like a pickup here. Aside from that, the two stressed syllables have half notes.
Line 2: Does the "sv" in "svalar" alliterate with the 's' in 'sandr' and 'saer'? The two plain s-words take half notes, svalar does not.
Line 3: The French rendered "ne upphiminn" as "Neu-phi-min", and it has the most complicated mapping of notes to syllables in the piece, of course it does. The French has 3 syllables with 6 notes; the Danish has 4 syllables (I think) to assign to the six notes. I am guessing that the half-note (an F) is what is properly assigned to the stressed syllable.
Line 4: All 3 'g' words take half notes.
Looking at just the words that alliterate AND take half-notes, I get:
F A
A A
F F
A G G
So if this is a 'melodic outline', to be filled in as the unstressed syllable arrangement requires it, it's on a per-stanza basis, not a per-line basis. Which makes sense, because singing the same melody over and over and over for each verse is already a lot; if it was the same melody for every line, it would be ridiculous.
Interestingly, the final note corresponding to a stressed syllable is a G - the key signature is a B-Flat, so F Major. If this were the usual final note, I'd say, yup, Dorian mode! As it is, the piece actually ends on an F. F also seems to play an important structural role, much more than I would expect if this were really a Dorian piece.
The B-flat actually gets played in the second line (second syllable of 'sandr' and the 'ne' that follows) so, if this was accurately recorded by the collector, it's not a Lydian mode piece (where the B would be natural).
The range is from E to B, a fifth, which fits with other things I've read about epic songs often having that sort of very narrow range. Also fits on either a lyre or even a kantele.