That's life across the channel (4,2,3)

I believe the answer is:

cest la vie

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'that's life' is the definition.
(I've seen this before)

I can't explain the remainder of the clue.

(Other definitions for cest la vie that I've seen before include "Whatever will be will be" , "There's nothing we can do about it!" , "That's life for the French (1'3,2,3)" , "Vets Alice (anag) - French expression of resignation" .)

I've seen this clue in The Daily Express.

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