Fishing net put straight across small French river (5,5)

I believe the answer is:

purse seine

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

'fishing net' is the definition.
(purse seine is a kind of fishing net)

'straight across small french river' is the wordplay.
'straight across small' becomes 'purse' (I can't justify this - if you can you should give a lot more credence to this answer).
'french river' becomes 'seine' (I've seen this in another clue).
'purse'+'seine'='PURSE-SEINE'

'put' acts as a link.

Can you help me to learn more?

(Another definition for purse seine that I've seen is " net?".)

I've seen this clue in The Times.

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