Crossword Genius

Empty bottle, one flaoting in a French river, cold at the head (4,6)

Ross

I believe the answer is:

dead marine

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

'empty bottle one flaoting in a french river' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'cold at the head' is the wordplay.
I cannot quite understand how this works, but
'cold' could be 'dead' (similar in meaning) and 'dead' is located in the answer.
'at' could be 'in' (synonymous in some cases - eg at school, in school) and 'in' is found within the answer.
The remaining letters 'mare' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

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