Covering church and French chopper (7)
I believe the answer is:
hatchet
'chopper' is the definition.
(something which 'chops')
'covering church and french' is the wordplay.
'covering' becomes 'hat' (hat is a kind of covering).
'church' becomes 'ch' (common abbreviation).
'and french' becomes 'et' ('and' in French).
'hat'+'ch'+'et'='HATCHET'
(Other definitions for hatchet that I've seen before include "Hand-held chopping instrument" , "Sort of job" , "Tomahawk" , "Light axe" , "chopper" .)