Ignore information rejected by the French court (7)
I believe the answer is:
neglect
'ignore' is the definition.
(synonyms)
'information rejected by the french court' is the wordplay.
'information' becomes 'gen' (gen can informally mean information).
'rejected' is a reversal indicator.
'by' says to put letters next to each other.
'the french' becomes 'le' ('the' in French).
'court' becomes 'ct'.
'gen' back-to-front is 'neg'.
'neg'+'le'+'ct'='NEGLECT'
(Other definitions for neglect that I've seen before include "Fail to pay due attention to (7)" , "Disuse" , "Leave undealt with" , "Omit by carelessness" , "Fail to care for properly" .)