The French cross is careless (3)
I believe the answer is:
lax
'careless' is the definition.
(synonyms)
'the french cross' is the wordplay.
'the french' becomes 'la' (one of the French words for 'the').
'cross' becomes 'x' (an X is a cross).
'la'+'x'='LAX'
'is' acts as a link.
(Other definitions for lax that I've seen before include "Loose, careless" , "Not strict or conscientious" , "Insufficiently strict" , "Casual" , "Careless or slack" .)