The military guys from Algeria had already put their hands on Corsica, plus, the iminent threat of the landing on the shores of Southern France (or via an aeria

The military guys from Algeria had already put their hands on Corsica, plus, the iminent threat of the landing on the shores of Southern France (or via an aerial operation, can't remember exactly) of said military forces was heavily used by de Gaulle during the negotiations that got him into power.