Garment puts one of the French into spasm (5)
I believe the answer is:
tunic
'garment' is the definition.
(historical type of garment)
'one of the french into spasm' is the wordplay.
'one of the french' becomes 'un' (I am not sure about this - if you are sure you should believe this answer much more).
'into' means one lot of letters goes inside another.
'spasm' becomes 'tic' (tic is a kind of spasm).
'un' going within 'tic' is 'TUNIC'.
'puts' is the link.
Can you help me to learn more?
(Other definitions for tunic that I've seen before include "Schoolgirl's dress" , "Smock" , "Short uniform coat" , "Belted coat" , "Policeman may be in one" .)