Ayto doesn't expound how attendre signifies "to wait" in French. Unquestionably, directing one's attention to something differs from waiting. E.g. when people wait in line or for their flight, they aren't directing their attention to anything. They can play with their phone, daydream, gawk at the sky, prattle with other queuers, etc...
Etymologically, attend means ‘stretch to’. It comes originally from Latin attendere, a compound verb formed from the prefix ad- ‘to’ and tendere ‘stretch’ (a descendant of an Indo-European base *ten-, *ton- ‘stretch’ which also produced, among others, Latin tenēre ‘hold’ – source of English contain, maintain, obtain, etc – and English tendon, thin, and tone). By metaphorical extension ‘stretch to’ became ‘direct one’s attention to’, which was the original meaning of the verb in Old French atendre and subsequently in English. The sense ‘take care of’ developed in the 15th century, ‘be present’ much later, in the 17th century. The noun derivative attention  comes from Latin attentiō. Tend meaning ‘look after’ comes mainly from attend, but also partly from intend, in both cases with loss of the first syllable.
Word Origins (2005 2e) by John Ayto. p 41 Right column.
Wait originally meant ‘look, spy’. But the notion of remaining in hiding, keeping a watch on one’s enemies’ movements led via the sense ‘remain, stay (in expectation)’ to, in the 17th century, ‘defer action’. The word was borrowed from Old Northern French waitier, which was itself a loanword from prehistoric Germanic *wakhtan (ultimate source also of English waft). This in turn was formed from the base *wak-, which also produced English wake, watch, etc. The sense ‘serve food at table’ emerged in the 16th century from an earlier ‘attend on’.
Op. cit. p 538 Right column.