Probably not much on a short term. I think Pompidou would have more difficulties to claim De Gaulle's political heritage, since his own success after 1968 was very much dependant from De Gaulle's decline, especially among right-wing Gaullists. A success in the 1969 (it's 1969, not 1968) referendum would lower Pompidou's position, compared to more orthodox Gaullists (especially Chaban-Delmas). However, De Gaulle would still die the year after.
The consequences are more interesting on a long term :
-the Senate as we know it disappears, which fulfills De Gaulle's dreams (the Senate was quite Anti-Gaullist). The National Assembly becomes the only legislative assembly, the new Senate having only advisorial powers. It ironically may serve the Left, the Senate being structurally dominated by the Right, since the electoral process favors the rural constituencies. You'll note that, historically, unicameralism in France was a radical idea since the Revolution.
-the Regions gain many powers, which is a tremendous shift from the jacobin culture of Gaullism. Devolution, twelve years before (historically, the Regions became local authorities in 1982)
-Pompidou will have less chances to succeed De Gaulle. If no President Pompidou, probably no President Chirac. Jacques Chirac became an important politician when being minister of the Interior, then for Argiculture during the Pompidou presidency, then he managed to seize control of the UNR Gaullist party after Pompidou's death. I guess that Chaban-Delmas, perhaps Debré, would have been more probable heirs to De Gaulle, which might butterfly Chirac (and maybe Sarkozy, for that matter). More traditional Gaullists such as Robert Boulin or Philippe Seguin would be the next rising stars.
-the 1971 presidential elections (De Gaulle died late in 1970) would be something interesting. The Moderates behind Giscard might attempt a "coup" with Pompidou to take the Presidency to the orthodox Gaullists (I'm pretty sure Chaban would have been the Gaullist candidate). You might have either a Chaban presidency or a Giscard-backed Pompidou presidency. I doubt the Left would have done better than in OTL. Note that if Chaban is President, the UK might wait a few more years to enter the EEC (not that it would have bothered quite a few gentlemen on this board, anyway).
-Assuming, however, that Pompidou is not elected in 1971 (and that he still dies in 1974), I'm pretty sure that Mitterrand would have been elected in 1978 : the crisis would have weakened the Right and the Left was on a roll after the huge win of the 1977 municipal elections (cities that had never been governed by the Left and were considered safe for the Right, notably in the West, went PS. Many of them still are, incidently).