Big car pulling up short in French region (8)
I believe the answer is:
limousin
'french region' is the definition.
(Limousin is an example)
'big car pulling up short' is the wordplay.
'big car' becomes 'limousine' (I've seen this before).
'pulling up short' means to remove the last letter.
'limousine' with its final letter removed is 'LIMOUSIN'.
'in' acts as a link.
(Other definitions for limousin that I've seen before include "French breed of cattle" , "French district" , "Cow" , "Kind of stock" .)