Law officer out of bed greeting new French prince (7)

I believe the answer is:

dauphin

I'm a little stuck... Click here to teach me more about this clue!

'french prince' is the definition.
'dauphin' can be an answer for 'prince' (dauphin is a kind of prince). I am not sure about the 'french' bit.

'law officer out of bed greeting new' is the wordplay.
'law officer' becomes 'da' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'out of bed' becomes 'up' (synonyms).
'greeting' becomes 'hi' (hi is a kind of greeting).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'da'+'up'+'hi'+'n'='DAUPHIN'

Can you help me to learn more?

(Other definitions for dauphin that I've seen before include "King of France's heir" , "former royal" , "French king's eldest son" , "Eldest son of the French king" , "French royal heir" .)

I've seen this clue in the Sydney Morning Herald.

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