A lady leading the European Union? See you in France! (5)

I believe the answer is:

adieu

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'you in france' is the definition.
The definition suggests a singular noun which matches the answer.

'a lady leading the european union?' is the wordplay.
'a lady' becomes 'adi'.
'leading' means one lot of letters go next to another.
'the european union?' becomes 'eu'.
'adi'+'eu'='ADIEU'

'see' is the link.

Can you help me to learn more?

(Other definitions for adieu that I've seen before include "the last word in France" , "Farewell, adios" , "Goodbye, monsieur" , "Farewell (French)" , "Farewell, Monsieur!" .)

I've seen this clue in The Times.

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