Outburst showing so much of the French spirit! (7)
I believe the answer is:
tantrum
'outburst' is the definition.
(I've seen this before)
'so much of the french spirit' is the wordplay.
'so much of the french' becomes 'tant' ('so much' in French).
'spirit' becomes 'rum' (alcoholic spirit).
'tant'+'rum'='TANTRUM'
'showing' acts as a link.
(Other definitions for tantrum that I've seen before include "Pet, temper" , "petulant outburst" , "Paddy" , "Child's outburst of bad temper" , "Spoilt brat's fit" .)