The word 'textile' is from Latin, from the adjective textilis, meaning 'woven', from textus, the past participle of the verb texere, 'to weave'.
The word 'fabric' also derives from Latin, most recently from the Middle French fabrique, or 'building, thing made', and earlier as the Latin fabrica 'workshop; an art, trade; a skilful production, structure, fabric', which is from the Latin faber, or 'artisan who works in hard materials', from PIE dhabh-, meaning 'to fit together'.
The word 'cloth' derives from the Old English clað, meaning a cloth, woven or felted material to wrap around one, from Proto-Germanic kalithaz (compare O.Frisian 'klath', Middle Dutch 'cleet', Dutch 'kleed', Middle High German 'kleit', and German 'kleid', all meaning "garment")