Serious French article’s circulating, though one line’s missing (9)
I believe the answer is:
unsmiling
'serious' is the definition.
(thesaurus)
'one line's missing' is the wordplay.
'one' becomes 'un' (northern English dialect form of 'one').
'line's missing' becomes 'smiling' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'un'+'smiling'='UNSMILING'
'french article's circulating though' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Another definition for unsmiling that I've seen is " Serious, unfriendly".)