Current French state is often called the Fifth Republic. What were the changes made in 1958 to deserve considering it a new form of government?
It was also preceded by a republic, unlike other times when a republic was re-established after periods of monarchy or foreign ocupation.
The changes between the Fourth and the Fifth Republic are very important in the way the power is distributed.
To understand what was done, we have to look into why this constitutionnal change happened. The IIIrd and IVth Republics were plagued with governmental instability caused by the fragmentation of the political spectrum with a lot of political parties that rended governing the country difficult. During the twelve years it lasted, 24 governments succeeded.
So the goal of the Vth republic was to enable the government to govern, even without a strong majority, because it was assumed that no strong majority would be able to be found. For that, they wanted to prevent the Parliament to interfere in the Government's activities.
Among other things, the Constitution of 1958 brought to the table differents points to fulfill that Parliament's rationalisation ("rationalisation du Parlement" in French):
All that was furthermore changed when in 1962, the General de Gaulle, who was the President at the time, decided to use art 11 to revise the constitution and get the President elected directly by the People, and not indirectly through great electors. It is still a contested move because to revise the Constitution you should use art 89, but that procedure necessitate the accord of the Parliament. The Consitutionnal Council chose to decline his competence to review this unusual (and for some unconstitutionnal) procedure.
Since then, we have what we call the majority fact ("fait majoritaire") which means that every president, once elected, had a majority in the National Assembly. This majority gets it's legitimity through the new President, and therefore, the President become really important because the Government rely on him for the majority. But in the text, the President doesn't have much power, nearly all executive power are held by the Prime Minister.
France is still a Parliamentary Republic, the form of government wasn't change. What changed was the organisation of that form of government, to make it stable and rulable.