'non-fringed' is formed from the English negative prefix 'non-' (ultimately from Latin 'non' meaning 'not') combined with 'fringed', the past-participial adjective of 'fringe'.

'fringe' entered English from Old French 'fringe' (or 'frange') in Middle English, and 'fringed' developed as the adjective/past participle; the modern compound 'non-fringed' is a straightforward negation of that adjective.

Originally 'fringe' referred to an ornamental border (threads, tassels); 'fringed' meant 'having such a border', and 'non-fringed' came to mean 'lacking that border' without additional figurative senses.