Last letter in French is showing enthusiasm (4)
I believe the answer is:
zest
'enthusiasm' is the definition.
(zest can mean enthusiasm or eagerness)
'last letter in french is' is the wordplay.
'last letter' becomes 'z' (in the alphabet).
'in french is' becomes 'est' ('is' in French).
'z'+'est'='ZEST'
'showing' is the link.
(Other definitions for zest that I've seen before include "Verve, gusto" , "Tang; gusto" , "Go" , "Relish, enthusiasm" , "added flavour" .)