Worked out as French duke in action (7)
I believe the answer is:
deduced
'worked out' is the definition.
(I've seen this before)
'french duke in action' is the wordplay.
'french duke' becomes 'duc' ('duke' in French).
'in' indicates putting letters inside.
'action' becomes 'deed' (deed is a kind of action).
'duc' put within 'deed' is 'DEDUCED'.
'as' acts as a link.
(Other definitions for deduced that I've seen before include "Gathered" , "Inferred" , "Worked out by reasoning" , "Came to logical conclusion like Sherlock" , "Arrived at by reasoning" .)