After love, one is overwhelmed by French rejection — it's a tear-jerker (5)
I believe the answer is:
onion
'a tear-jerker' is the definition.
(cutting onions can make you cry)
'after love one is overwhelmed by french rejection' is the wordplay.
'after' is a charade indicator (letters next to each other).
'love' becomes 'o' (love means zero in tennis).
'one' becomes 'i' (Roman numeral).
'is overwhelmed by' is an insertion indicator (inserted letters get absorbed or overwhelmed).
'french rejection' becomes 'non' ('no' in French).
'i' inserted into 'non' is 'nion'.
'o' put next to 'nion' is 'ONION'.
'it's' is the link.
(Other definitions for onion that I've seen before include "reason for tears" , "Bulbous vegetable" , "Type of allium" , "Head (slang); vegetable" , "it can bring tears" .)