There are a couple of things that happened, but mainly there's one thing, the rise of colonial rebellion.

During WW2, France fell and resulted in one terrible thing, Free France was fighting for France and left the colonies to their own devices. These colonial holdings generally fought with the Allies (with North Africa siding with Vichy due to proximity and German invasion later on to support the Italians). With Free France fighting the Axis, the colonial holdings got used to being left alone. Combined with this, France was giving fuel to anti-French forces within these colonies due to neglect and long building anti-French sentiment building from the turn of the 20th century.

With France liberated, the focus was on the White French that fought over the years, pushing aside the many non-white soldiers that fought and bled over the years. Charles de Gaulle even told General Leclerc to find more white soldiers since many of his soldiers were from Central and North Africa. Naturally this would also alienate many of those soldiers that were suddenly finding themselves as inferior to the few white French that fought with them, something General Leclerc voiced.

So, with France secure, the French wanted to return back to normal but as usual that wouldn't happen. Many of the colonies had been pushing France away, including major players like French Indochina and Algeria in the early to mid fifties. In the attempt of trying to neutralize these threats, the wars would turn against France and cause the public opinion to change against them in favor of independence, leading to a Constitutional Crisis that stems from the Algerian crisis.

With a new Constitution led by Charles de Gaulle, France would politically settle in respect to their governmental position, but this doesn't mean that France is done. De Gaulle wanted to return France into a major world power. This would lead to many things, such as a strong military (which is still one of the premier forces in Europe and a major arms dealer in the world), a strong focus on atomic power to ensure no fuel dependency (as France has a high number of nuclear power plants), and a strong political position in the new Post-War/Post Independence Crisis Europe. All of these are major tenants of Gaullism that would become a major political ideology within France that was neither truly left or right. De Gaulle was more conservative but still asserted republican ideology within France and a unified ideal of France that is more patriotic than ideological.

This focus on a strong, unified, and powerful France would of course have problems with many other groups. France "left" NATO but only because of the American command structure that effectively had America as the leader of NATO. De Gaulle didn't like that and an American focus on equipment so France effectively pulled out of NATO, but never truly did as they made agreements with NATO to support NATO if there was any attack made by the Soviets.

The 20th Century wasn't the kindest to France. France hadn't industrialized as quickly as the rest of Europe and lost the population advantage they had during the early 19th century. Combined with the extreme loss of life during the First World War and the general ineffective interwar government made France ripe to be easily defeated during the Second World War. However France would recover thanks to de Gaulle.

Edit: Forgot Sources

Free France's Lion: The Life of Philippe Leclerc, de Gaulle's Greatest General by William Moore.

France and the French: A Modern History by Rod Kedward