Nazi and GI crazy over her, French elegant creature (6,7)

I believe the answer is:

indian gazelle

'elegant creature' is the definition.

'nazi and gi crazy over her french' is the wordplay.
'crazy' indicates an anagram.
'over' is a charade indicator (letters next to each other).
'her french' becomes 'elle' ('her' in French).
'nazi'+'and'+'gi'='naziandgi'
'naziandgi' is an anagram of 'indiangaz'.
'indiangaz'+'elle'='INDIAN GAZELLE'

I've seen this clue in The Guardian.

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