Illuminated about one Frenchman, to a extent (5)
I believe the answer is:
limit
'to a extent' is the definition.
(limit is a kind of extent)
'illuminated about one frenchman' is the wordplay.
'illuminated' becomes 'lit' (synonyms).
'about' is an insertion indicator.
'one' becomes 'I' (Roman numeral).
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'i'+'m'='im'
'lit' enclosing 'im' is 'LIMIT'.
(Other definitions for limit that I've seen before include "Confine to specific boundary" , "Place bound on" , "Constrain" , "As far as something can go" , "Breaking point" .)