Onset of weariness strikes a French religious festival (7)
I believe the answer is:
whitsun
'religious festival' is the definition.
(Whitsun is a religious festival)
'onset of weariness strikes a french' is the wordplay.
'onset of' says to take the initial letters.
'strikes' becomes 'hits' (hit can mean to strike).
'a french' becomes 'un' ('a' in French).
The initial letter of 'weariness' is 'w'.
'w'+'hits'+'un'='WHITSUN'
(Other definitions for whitsun that I've seen before include "Wins hut on short Christian Sabbath" , "Spring festival" , "Pentecost season" , "Holy Spirit festival" , "Period seven weeks after Easter" .)