Puppet governments are not governments. The pattern of Roman client states was being followed here.
Then the same applied to all of the Captive Nations behind the Iron Curtain during the Cold War.
There was no break in government from the time when France was still fighting until the occupation by the British and Americans (and their ‘Free French’ puppet government). Indeed, de Gaulle, recognizing the threat that the resistance was to his self-appointed leadership arranged for the Germans to liquidate a large body of the resistance in the Vercors area.