'many-coloured' is a compound of the adjective 'many' and 'coloured'. 'many' originates from Old English 'manig' (meaning 'many'); 'coloured' comes via Old French 'colour'/'colore' from Latin 'color' (meaning 'hue, tint').

'many' descended from Old English 'manig'; 'colour' entered English from Old French (medieval forms like 'colour'/'colur') ultimately from Latin 'color'. The compound form (e.g. Middle English spellings such as 'manie-colour'd' or similar) developed into the modern hyphenated 'many-coloured'.

Initially the parts meant 'many' + 'hue/tint'; the compound has retained the basic sense of 'having many colours' into modern usage.