Rushed out of France (3)
I believe the answer is:
ran
'rushed' is the definition.
'of france' is the wordplay.
'of' says the answer is hidden in the clue.
'RAN' is hidden in the letters of 'france'.
'out' is the link.
(Other definitions for ran that I've seen before include "Managed; hurried" , "Administered" , "11 on foot" , "Managed; raced" , "was in charge" .)