'narrow-footed' is a modern English compound formed from the adjective 'narrow' and the past-participial adjective-forming suffix on 'foot' ('footed'), literally meaning 'having narrow feet'.

'narrow' comes from Old English 'nearu' meaning 'narrow, close'; 'footed' derives from Old English 'fōt' (foot) plus the adjectival suffix '-ed'. The compound arose in Modern English by straightforward combination of these elements.

Initially both elements meant the same physical senses ('narrow' = small in width; 'foot' = the foot), and the compound's meaning ('having narrow feet') is a direct continuation of those senses with little semantic shift.