In French, starts to nag us, implying boredom (5)
I believe the answer is:
ennui
'boredom' is the definition.
('ennui' can be a synonym of 'boredom')
'in french starts to nag us implying' is the wordplay.
'in french' becomes 'en' ('en' can be French for 'in' e.g. en France).
'starts to' suggests taking the first letters.
The first letters of 'nag us implying' is 'nui'.
'en'+'nui'='ENNUI'
(Other definitions for ennui that I've seen before include "Boredom in France" , "What's tedious and instils such listlessness" , "Effect of boredom" , "Feeling of listlessness" , "having nothing to do" .)