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.
It should be noted that some of the main people who called to view it as a coup were people from other parts of the political spectrum who had other ideas of how it should happen and who should end up in power, including Mitterand (who ended up president of the 5th in 1986). These people however were also for the end of the 4th.