Well she's certainly not soul.
If she was black, she still wouldn't be soul. Of course people would call her soul, but then that would just be a Rihanna-is-R&B tea.
"Don't You Remember" has some folk influences, but that's the only one I can think of that sounds like a folk song. Adele's music is a mixture of different genres, and one of those genres is soul. "Cold Shoulder" and "I'll Be Waiting" sound like soul songs to me. The latter kind of sounds like something that could have been on a Dusty Springfield album.
