Had De Gaulle won the referendum and stayed in office, he could have died in November 1970 as in OTL, or finished his term in December 1972.
Had he died in office in November 1970, he would have been succeeded, not by the President of the Senate, but by the Prime Minister (let’s not forget that the 1969 referendum also changed the constitutional procedure in case of a vacancy).
De Gaulle’s PM, Maurice Couve de Murville, would then have been Acting President, until an election could be organized, either in December or early January 1971. It is highly unlikely that Couve de Murville would have been a candidate. On the other hand, Pompidou, the former Prime Minister between 1962 and 1969, almost certainly would have ran. At this time, his illness was still in its early stages and Pompidou would have thought that he was strong enough to overcome it.
Had he run, he would have won easily. Then, things would have continued more or less like in OTL. Would Pompidou still have appointed Jacques Chaban-Delmas Prime Minister (as he did in 1969 in OTL)? In which case Chaban could still have been in office when the President died, and as Acting President, would have been in a much better position to succeed him that he was in OTL. Giscard d’Estaing, having opposed De Gaulle in the 1969 referendum, would probably not have had the successful ministerial carreer that he had between 1969 and 1974 in OTL. So Chaban almost certainly would have been the gaullist party’s candidate.
Would Chaban have won the election? Mitterrand, sole candidate of the Socialist and Communist parties, was an effective campaigner, not as good as Giscard, but definitely better than Chaban (after all, in OTL, he lost to Giscard by only 400,000 votes). I think Mitterrand would have won, thus becoming President 7 years earlier than in OTL.
Had De Gaulle lived long enough to finish his term (December 1972), things could have been different, depending on Pompidou’s health. By late 72, early 73, the side effects of his medical treatment became obvious (see pictures of his meeting with Nixon in Iceland in May 1973) and everybody knew that he was seriously ill. I don’t think he would have been in a position to run.
Who else could have?
Maurice Couve de Murville (supposing he was still Prime Minister, which is likely) would almost certainly not even have tried it.
Valéry Giscard d’Estaing? Unlikely (De Gaulle would have made sure he was kept out of the government and he would therefore be seen as too young at 46, and lacking of experience).
Michel Debré (De Gaulle’s PM between 1959 and 1962): possible – he was considered a faithful gaullist and would have had the support of the UDR (the gaullist party). I doubt very much he could have won the election against Mitterrand, though.
Edgar Faure, twice head of government during the Fourth Republic, minister of Agriculture, then of National Education under De Gaulle, brilliant, funny, good campaigner (and at some point candidate to Pompidou’s succession in OTL): a possible candidate; in my opinion the one with the better chance to defeat François Mitterrand in a presidential election.
Jacques Chaban-Delmas: a faithful Gaullist, a hero of the Resistance – but in a world where De Gaulle remained in office until 1972, he would not have been Prime Minister, and would lack governmental experience. Plus, were Debré to run, Chaban would almost certainly have deferred to him.
So in my opinion, had Charles De Gaulle won the referendum in 1969 and stay in power (up to his death or until the end of his term), there is a pretty good chance that François Mitterrand and the Left would have come to power years ealier than in OTL.
We would have had a Socialist/Communist government and a political programme not very different from the one that was followed in OTL’s early Eighties: social reforms, nationalisations, abolition of the death penalty. Mitterrand’s politics would have been maybe a little bit more radical than they were in OTL, because in 1972-1974, the Communist Party was stronger than it was in 1981, and of course the international context was different…