Goddamn, you stole my idea! As I'm working a bit on it, I have to point some of these:
-The Algeria War was completely over with the Evian Accords which were signed in March, Salan had been arrested in April, and the rest of the OAS Staff was on the run or arrested. The assassination attempt on De Gaulle was part of a terrorist campaign to make some sort of "gallant last stand" from the Algérie Française proponents, and would have led to a massive crackdown against the OAS, not a coup: even if many French high ranking officers were still put out by Algerian independance, the complete failure of the Generals' Putsch the previous year would have forced them to back down.
-The 1962 presidential campaign, due to the Constitution then, would have been decided by an electoral college composed of prominent elected politicians. Pompidou was Prime Minister for less than six months by August 1962 and was a political nobody then, with no previous executive experience: Jacques Chaban-Delmas had the military record, the experience as Mayor of Bordeaux and was quite young, Robert Debré had been tired by four years as Prime Minister and was known for his Algérie Française personnal positions. Don't forget that the French Communist Party was making more than 20% in elections by the time, but they will put forth a sacrificial lamb candidate for the biased structure that the electoral college is. Most of the conservative right which then composed the French elected landscape, seeing no providential man as De Gaulle among the Gaullists, would have aligned behind a moderate-to-conservative politician: I think of Pierre Pflilmin, last Prime Minister of the Fourth Republic, or Antoine Pinay, former Minister of Finance.