Object, being in French dungeon at the beginning (3)
I believe the answer is:
end
'object' is the definition.
(end is a kind of object)
'in french dungeon at the beginning' is the wordplay.
'in french' becomes 'en' ('en' can be French for 'in' e.g. en France).
'at the beginning' indicates taking the first letters.
The initial letter of 'dungeon' is 'd'.
'en'+'d'='END'
'being' is the link.
(Other definitions for end that I've seen before include "Conclusion or purpose" , "Conclusion, finish" , "Time to break-up (3,2,4) - See 12" , "Remainder" , "Conclusion or goal" .)