The French overwhelmed by roach-spread disease (7)
I believe the answer is:
cholera
'disease' is the definition.
(cholera is a kind of disease)
'the french overwhelmed by roach-spread' is the wordplay.
'the french' becomes 'le' ('the' in French).
'overwhelmed by' indicates putting letters inside (inserted letters get absorbed or overwhelmed).
'spread' indicates anagramming the letters.
'roach' with letters rearranged gives 'chora'.
'le' put into 'chora' is 'CHOLERA'.
(Other definitions for cholera that I've seen before include "serious illness" , "Acute intestinal infection from contaminated water or food" , "Acute infection caused by contaminated water or food" , "bacterial disease" , "could kill you" .)