Discover area covered by the French navy ... (5)
I believe the answer is:
learn
'discover' is the definition.
(synonyms)
'area covered by the french navy' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'covered by' means one lot of letters go next to another (on top of in a down clue).
'the french' becomes 'le' ('the' in French).
'navy' becomes 'RN' (abbreviation for Royal Navy).
'a' after 'le' is 'lea'.
'lea'+'rn'='LEARN'
(Other definitions for learn that I've seen before include "Study or digest" , "Study - find out" , "Take in" , "be taught a lesson" , "Become aware of" .)