'splay-footed' is a Modern English compound formed from 'splay' + 'foot' + the adjectival suffix '-ed'. 'splay' in English means 'to spread out' or 'to spread apart.'

'splay' itself goes back through Middle English (spleien/splayen) and is ultimately related to Old French terms meaning 'to spread' or 'to broaden.' The compound 'splay-footed' was formed in English by joining that sense of 'splay' with 'foot' to describe the orientation of the feet.

Initially the verb 'splay' meant 'to spread out' and, when combined with 'foot' as 'splay-footed,' it came to mean specifically 'having the feet turned outward'; this specific anatomical/gait sense has been maintained in modern usage.