Fate of French mistress's last minute (7)
I believe the answer is:
destiny
'fate' is the definition.
('destiny' can be a synonym of 'fate')
'of french mistress's last minute' is the wordplay.
'of french' becomes 'de'.
'last' suggests the final letters.
'minute' becomes 'tiny' (I've seen this before).
The final letter of 'mistresss' is 's'.
'de'+'s'+'tiny'='DESTINY'
(Other definitions for destiny that I've seen before include "Ultimate fate" , "portion" , "Fortune" , "Lot" , "must?" .)