To the French embracing the German, goodbye! (5)
I believe the answer is:
adieu
'goodbye' is the definition.
('adieu' can be a synonym of 'goodbye')
'to the french embracing the german' is the wordplay.
'to the french' becomes 'au'.
'embracing' indicates putting letters inside.
'the german' becomes 'die' ('the' in German).
'au' going around 'die' is 'ADIEU'.
(Other definitions for adieu that I've seen before include "12 Down" , "Comment on leaving" , "Some say it when leaving" , "Fare thee well!" , "farewell message" .)