Rival business last to charm small Parisian men (10)
I believe the answer is:
competitor
'rival' is the definition.
(synonyms)
'business last to charm small parisian men' is the wordplay.
'business' becomes 'co'.
'last to' indicates one should take the final letters.
'small parisian' becomes 'petit' ('small' in French).
'men' becomes 'or' (I've seen this in other clues).
The last letter of 'charm' is 'm'.
'co'+'m'+'petit'+'or'='COMPETITOR'
(Other definitions for competitor that I've seen before include "Sporting contest entrant" , "rival trader?" .)