The problems that brought down the 4th Republic were problems that had already begun to corrode the 3rd Republic's stability. It also didn't help that the post-war period for France was particularly difficult, with its two most important colonies rising in open rebellion one after the other.
I suppose, though, that a forceful enough persona could have righted the ship of state and sailed them through the Algerian crisis without needing a constitutional reform, but that's mostly a matter of hand-waving someone like that in to power who isn't de Gaulle.