Officers with negative response from French company upset sergeant-major (3-4)

'officers' is the definition.
(short for non-commissioned officers)

'negative response from french company upset sergeant-major' is the wordplay.
'negative response from french' becomes 'non' ('no' in French).
'company' becomes 'co' (abbreviation).
'upset' says the letters should be written backwards.
'sergeant major' becomes 'SM' (abbreviation for sergeant major).
'sm' back-to-front is 'ms'.
'non'+'co'+'ms'='NON-COMS'

'with' acts as a link.