'resole' is formed in Modern English from the prefix 're-' (from Latin 're-', meaning 'again') + the noun 'sole' (from Old French/Anglo-French 'sole', ultimately from Latin 'solea' meaning 'sandal' or 'sole of the foot').

'sole' comes from Latin 'solea' via Old French; the verb was formed in English by adding the productive prefix 're-' to 'sole' to express doing the action again, producing 'resole'.

Initially and historically it has meant 'to put a new sole on a shoe' (i.e., 'replace the sole'), and this core meaning has remained stable into modern usage.