The celebrated Bataclan nightclub in the edgy 11th arrondissement of Paris was stiflingly hot and, even by its own standards, it was heaving.

A young crowd in the audience cheered, shouted, applauded and whistled – a not unusual racket in a cutting-edge venue that once hosted an unknown Edith Piaf and, more recently, Pete Doherty.

Avant-garde bands and cult rock stars pull them in here. After the music, the youngsters will spill out on to the streets and talk will invariably turn to late-night parties and where to go next.

Last week, however, the Bataclan hosted an unlikely headline act: a balding, bespectacled man in a spectacularly dull suit whose nickname is Mr Normal. And the excited chatter was of political parties, where next for France, and who will triumph in the second, deciding round of the Socialist party primaries, which takes place today.

"François, president. François, president," shouted the crowd, supporting their favourite presidential candidate, François Hollande. Outside on the pavement, others watched on a hastily installed television screen.

When France's Socialists announced months ago that for the first time they would hold American-style primary elections to choose a presidential candidate, the process promised to be worthy, admirable even, but dull. Instead, it appears to have kindled the political fire in a new generation of voters.

It helped that among the six candidates were two newish, youngish faces: Arnaud Montebourg, 48, the surprise runner who beat the Socialists' 2007 presidential candidate, Ségolène Royal,to take third place in the first round last Sunday, and Manuel Valls, 49, who finished just behind Royal. The injection of new blood into a party once said to be run by "elephants", combined with profound disappointment in the country's current leaders, and in particular the deeply unpopular Nicolas Sarkozy, appears to have inspired a wave of youngsters on the left. After 17 years of rightwing rule, they are ravenous for change.

Their grandparents' generation took to the streets, throwing up barricades and calling for education reforms and an overthrow of the "old" society in the May 1968 student uprisings .

Their parents' generation came of age during the 14-year leadership of Socialist François Mitterrand, the Fifth Republic's only Socialist president.

Today's young Socialists are hoping for their own revolution during the presidential vote next May. They also worry about education and the environmental issues that came to the fore in the 1980s, but above all they are galvanised by the worsening economic crisis and fears of how it will affect their chances of getting a job and affording a place to live.

Florence Assan, 21, a medical student who has been campaigning for Hollande's main rival for the party nomination, Martine Aubry, says the Socialist primaries have given a voice to the young.

Unusually, the primary vote was opened to any adult who paid €1 to the Socialist party and pledged support for leftwing values, but also to teenagers aged 15-18 if they were registered with Young Socialist organisations. "Most of our lives all we have known is the right in power," says Assan. "Now we want change. We want politics to put people – including young people – at its heart."

Sylvain Lobry, 20, an engineering student, agrees. "They said we were the generation that had turned its back on politics, but we have proved this wrong. The primary elections have proved this wrong. Even if we don't win [the presidential election], we will have done something extraordinary."

Hugo Hanry, 17, a lycée student, admits to being both impatient and confident for the result of the decisive second-round vote. He plans to vote for Aubry. "There is a renewal happening. Young people are becoming more and more interested, and more and more involved in politics. The Socialist party primaries have been an excellent democratic exercise," he says.

Last Sunday, at a polling station in the 3rd arrondissement of Paris, as left-leaning residents queued to vote in the first round, the atmosphere was almost festive. Families turned out with young children in tow, while jovial young Socialist activists hovered looking for an excuse to engage in conversation.

Asked about turnout or predictions, they tapped furiously into BlackBerrys and iPhones before producing answers correct to two decimal points. "This is the home run," said one young man.

To the primaries or the presidential? "Hopefully both," he replied.

At the Socialist party headquarters at Solférino on the Left Bank, Anthony Aly, spokesman for the Young Socialists Movement, and others he refers to as "camarades" were hunkering down behind the security gates as riot police gathered to see off a demonstration by members of the far-right National Front. "I'm told they're angry because we are giving foreigners the chance to vote in the primaries," he says, adding: "But the fact we opened up these elections for the first time to people who were not party members and young militants has provoked a great deal of interest among young voters."

Frédéric Dabi, of the French opinion pollsters Ifop, said surveys had shown that most of the 2.5 million French voters who turned out last Sunday to choose a Socialist candidate were over 50. However, he added: "It's true that because two of the candidates were relatively young, and because both François Hollande and Martine Aubry made issues concerning youngsters, like education, key to their campaigns, there has been a renewal of interest in politics among the young."

Back at the Bataclan, Hollande, the man who would be president, is responding to the adulation with republican France's equivalent of the royal wave, the two-handed bring-it-on gesture footballers use when they have scored. The crowd roar, jump to their feet and begin chanting again.

At 57, Hollande is no political spring chicken, having first been elected to parliament in 1988 after treading the well-worn route from the elite Sciences-Po college to the still more rarefied Ecole Nationale d'Administration – the hothouse for France's ruling elite. His chances of winning look good. His former partner and the mother of his four children, Ségolène Royal, has announced that she will vote for him, as have Valls and Montebourg.

Among the crowd at the club is Michel Mongkhoy, 23, an IT engineer, who talks with the zeal of a convert. In the last presidential election, Mongkhoy voted for Sarkozy. He says he will not be doing so this time. Although, like many French youngsters, he knows Sarkozy is not responsible for the global economic downturn that derailed many of the president's election promises, he still feels disappointed and betrayed. "He did nothing for us young people. He said he would and we put our hopes in him, but he didn't," he says.

His friend, Stéphane Blemus, 25, a law student at the Sorbonne, didn't vote for Sarkozy. He is not a card-carrying member of the Socialist party either, but he too is fired up with enthusiasm for Hollande. "Young people all over Europe are hungry for change and we have seen this in demonstrations in Greece and Spain. We are worried about endemic unemployment, about whether our diplomas will count for anything, about finding homes. We know the left cannot promise us a marvellous world, but we just want change.

"These primary elections have allowed the young to feel they are involved in the party and its programme and that we can change the rules of the game. That's important, because we are the new political generation."

Outside the Bataclan, with their hands still stinging from clapping so hard, Stéphane and Michel have missed Hollande's departure but, like loyal fans, they want their picture taken under the club's old-fashioned billboard on which FRANCOIS HOLLANDE has been spelt out in large black letters.

Michel says: "With this election, we feel we see the light at the end of the tunnel."