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' can be found hidden inside '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" .)