PARIS, DEC. 7 -- Despite France's robust prosperity, the public is showing rising anger and discontent toward both the Socialist government and the conservative opposition.

Strikes are becoming increasingly frequent as transport workers, students and even judges demand more money from the government. Ghetto riots are making people more nervous about North African immigrants. Opinion surveys show that more than half of voters think politicians are corrupt and that France thinks they rank with prostitutes as deserving of public trust.

Among the mainstream parties, nasty leadership feuds are making a mockery of slogans of political solidarity. While Socialist President Francois Mitterrand and his rival, Prime Minister Michel Rocard, undercut each other's authority, the center-right opposition alliance is floundering because of the clashing egos of neo-Gaullist leader Jacques Chirac and former president Valery Giscard d'Estaing.

Neither man dares to suggest the other may warrant support as the opposition's single candidate for the presidency when Mitterrand's second term expires in 1995. Nor can they decide how to cope with the challenge from Jean-Marie Le Pen, leader of the far-right National Front party that is steadily augmenting its presence by exploiting racial fears and sowing dismay with the squabbling moderates.

After Chirac pandered to nationalist sentiments by bluntly rejecting Giscard's vision of a United States of Europe this week, one of his most likely heirs quit Chirac's Rally for the Republic party in disgust and surrendered his seat in parliament. Michel Noir, the charismatic mayor of Lyon, the country's second-largest city, described the entire French political system as "sick" and said he could no longer tolerate the "partisan games that feed the anger and indifference of our citizens."

Noir appealed for other members of the French conservative establishment to follow his example. Within hours, popular former health minister Michele Barzach quit the party as well. "You have to know when to jump off a train that is leading nowhere," she said. "It's the only way for me to walk with my head high."

The resignations deprived the moderate right of two rising stars at a time when the electorate is demanding new faces and ideas to rejuvenate an encrusted political scene dominated by men like Mitterrand, Rocard, Chirac and Giscard who have held the leading roles in government and opposition for the past two decades.

Within the ruling Socialist Party, anxiety is growing that Mitterrand's presidency is showing fatigue after nearly 10 years in power. Commentators are comparing his plight more frequently with the restless public mood that characterized the last months in office of Charles de Gaulle and Britain's Margaret Thatcher, both of whom felt compelled to resign after their prestige and authority deteriorated.

Mitterrand's popularity has been sinking along with that of Rocard as feuding has escalated among their loyalists. The rivalry between the Socialist president and prime minister reached new heights nearly three weeks ago when Rocard's minority government barely survived a parliamentary vote of no confidence. Rocard's supporters accused Mitterrand of trying to persuade deputies to vote against Rocard to diminish his chances of succeeding the president.

Mitterrand has long favored Laurent Fabius, a former prime minister who is now president of the National Assembly, to inherit his mantle when he retreats from politics. But Rocard's enduring popularity, despite recent slippage, is considered one of the party's principal weapons in thwarting the right's hopes of winning the next parliamentary election in 1993.

Despite his dislike for Rocard, Mitterrand desperately wants to avoid seeing the right regain control of parliament and force him to repeat the "cohabitation" he endured from 1986 to 1988 while Chirac was prime minister.

Mitterrand still remains the most powerful political figure in France. Franz-Olivier Giesbert, editor in chief of the daily Le Figaro, compares him to Pablo Picasso for casting such a large shadow that he stunts the growth of those around him.

But even the president's close friends acknowledge that he has lost much of his passion, energy and interest in government lately. Socialist Party members grumble about his "creeping senility" and the aloofness that keeps him insulated from mundane realities.

In France, perhaps more than in any other Western democracy, political parties are defined by their leaders. One of Mitterrand's most crucial tasks is how to surmount a growing identity crisis among the Socialists. In France, as elsewhere in the West, many people are asking whether a party of the left can play a leading role in 21st century society yet remain faithful to founding principles that were largely discredited by the collapse of socialism in Eastern Europe.

When Rocard became prime minister 30 months ago, he quickly shored up his minority government by moving toward the center and recruiting moderate opponents to join the cabinet. Today only 22 of his 48 ministers are Socialists.

The prime minister has defined his centrist economic policy as "tempered capitalism," a term that has rankled diehard Socialist Party members but proven popular with the voters.

Rather than ideology, the public seems more concerned about corruption and the abuse of power. "Disdain for all of the mainstream parties is giving more votes to Le Pen," said political scientist Olivier Duhamel. Some surveys show Le Pen backed by up to 20 percent of voters.