Cinema shows first French field mine (7)
I believe the answer is:
fleapit
'cinema' is the definition.
(fleapit is a kind of cinema)
'first french field mine' is the wordplay.
'first' indicates taking the first letters.
'field' becomes 'lea' (I've seen this before).
'mine' becomes 'pit' (down the pit).
The first letter of 'french' is 'f'.
'f'+'lea'+'pit'='FLEAPIT'
'shows' acts as a link.
(Other definitions for fleapit that I've seen before include "Shabby old cinema" , "Scruffy cinema" , "shabby public building" , "Shabby place" , "Run-down cinema" .)