Ok here’s the deal. First off, this “Medieval sound” that you hear (more accurately a “Renaissance” sound) is only partially based on the scale, partially based on meter, and partially based on the even-note rhythm of the melody.
The scale is melodic minor (minor with a raised 6th and 7th degree ascending, natural minor descending although I don’t know offhand if it maintains this throughout). This is actually the standard minor scale in tonal music. (i.e. all “classical” music before the 20th century). In rock and pop and blues and 20th century music in general we’ve gotten used to hearing minor scales without that half-step between the 7th and the tonic. But in tonal music, that half-step is necessary to create a sense of gravity towards the tonic. (I realize this might sound like a lot of theoretical mumbo jumbo if you don’t understand the vocabulary. I don’t have too much time right now or else I would search for some musical examples online to show you what I mean).
The meter is 6/8 so you count it: 1 2 3 4 5 6
with accents on the 1 and 4. This is very common in early music, and not so common in popular music.
The rhythm of the melody is very straight 8th notes. The melody often justs runs right up and down the scale in step wise motion in these straight 8th notes. Every note is even: da da da da da da…
This is all very characteristic of Renaissance and Baroque music. After that melodies become more like themes (tunes which are hum-able and are more distinct in character).