"The First Time" is IMHO one of the finest love songs ever written, whatever arrangement is applied to it, from a capella to slushy strings. It was written by a man who was an actor, a playwright, a singer, a folklorist, a songwriter and a political activist, and sometimes a combination of any or all of those things at once. When he wrote that song, he did so as a man and a lover, but all his other experience was incorporated.
My belief is that, whatever genre a song or tune comes from, if it is interpreted and performed with thought and sincerity, that is all that matters, whatever the context. As long as it is correctly attributed to its original source, different interpretations can bring a song (or a whole body of work) to the notice of audiences that it might otherwise have passed by.
The true purpose of music and song is communication, not the self-indulgence of the performer. Labelling restricts that communication and can cause people to filter out things that could possibly bring them enjoyment.
Just for the record(!), I don't consider Roberta Flack's version "Soul" any more than Dave does, but then, define "Soul"!
Certainly that record, and Clint Eastwood's inclusion of it in "Play Misty for Me" brought this beautiful song to the notice of millions of people who would not have listened to Ewan's version (or the Kingston Trio's, for that matter). Does that make it "Film Music"?