French river ran out in the Middle East (5)

I believe the answer is:

marne

'french river' is the definition.
(I've seen this in another clue)

'ran out in the middle east' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'in the' indicates putting letters inside.
'middle east' becomes 'me' (abbreviation for Middle East).
'ran' is an anagram of 'arn'.
'arn' going inside 'me' is 'MARNE'.

I've seen this clue in The Globe and Mail.

Want a hint initially instead of a full solution? Install my app