A fine French cop periodically attends sick (9)
I believe the answer is:
afflicted
'sick' is the definition.
(similar in meaning)
'a fine french cop periodically attends' is the wordplay.
'fine' becomes 'f' (abbreviation).
'french cop' becomes 'flic' (I've seen this in another clue).
'periodically' indicates alternate letters (letters must be selected 'every so often').
The alternating letters of 'attends' are 'ted'.
'a'+'f'+'flic'+'ted'='AFFLICTED'
(Other definitions for afflicted that I've seen before include "Diseased; suffering" , "Troubled" , "Caused pain to" .)