At the time when this story was written, "schlicht" was used as a synonym for "glatt" and means non-curly in context with hair. See, for example, the discussion at
https://www.jstor.org/stable/25754886 You may also hear elderly ladies call "schlicht" and "kraus" knitting (plain stitch and purl) what is nowadays called "glatt/rechts" or "kraus/links". Literally, "schlichtes Haar" is just "straight hair", but I am not sure if this is the best translation with appropriate connotations for your context.