The French bilge is possibly quite readable (7)

I believe the answer is:

legible

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'quite readable' is the definition.
'legible' can be an answer for 'readable' ('legible' can be similar in meaning to 'readable'). I am not certain of the 'quite' bit.

'the french bilge is possibly' is the wordplay.
'the french' becomes 'le'.
'is possibly' indicates an anagram.
'bilge' is an anagram of 'gible'.
'le'+'gible'='LEGIBLE'

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(Other definitions for legible that I've seen before include "Well written" , "Clear enough to read" , "Easy to read" , "Decipherable" , "Good characters are" .)

I've seen this clue in the Evening Standard.

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