They are riding high in the polls, sensing a chance to win their first presidential vote since 1988 and buck a trend across Europe in which the left is in retreat.

But France's Socialists are gearing up for a bruising battle against Nicolas Sarkozy in next spring's presidential election, worried that voters do not trust them to handle the financial crisis.

With the 2012 presidential race wide open, the Socialists' first hurdle is to find a candidate both charismatic and ruthless enough to defeat the genius of Sarkozy on the campaign trail and in the televised debates.

François Hollande, the wise-cracking, self-styled "ordinary guy" of French politics, is the early frontrunner, deploying humour and economic nous in equal measure at this weekend's conference in La Rochelle.

A former Socialist party leader and MP in rural central France, Hollande, 57, has gone on a crash diet and smartened up his suits after splitting from his partner, the former presidential runner Ségolène Royal. Famous for his jokes – which charmed audiences at the party conference – Hollande is seen as the most presidential candidate and the most trusted on economic matters. He has an economics background and has positioned himself on the centre-left.

"If we don't dominate money, money will dominate us," Hollande said in his conference speech, arguing that his priorities were tax reform, helping France's desolate and largely unemployed youth, and kick-starting growth through careful state investment.

Against him is Martine Aubry, 60, the mayor of Lille and the first woman to lead the Socialist party. An architect of the 35-hour week, she is seen as a defender of leftwing values and a "caring" society. One T-shirt slogan among supporters read: "Yes we care".

She told the party conference that austerity alone would not work and French economic woes must be resolved by tackling root issues of "education, employment and sustainable development". She is seen as austere, less charismatic and less hungry for power. She jumped into the race late to replace the favourite Dominique Strauss-Kahn, viewed as dead politically after the alleged attempted rape of a New York hotel-maid.

Royal is still in the race, in third position.

The left may be in decline across Europe and are likely to lose in Spain this autumn, but all recent polls show that the Socialists would win if the election were to take place now. And yet party activists are extremely cautious.

After the euro zone debt crisis raised investor doubts about France's prized triple-A credit rating and unemployment last week soared to the highest level since Sarkozy's election, the economy is at the heart of the presidential race.

Sarkozy's latest initiative for a temporary tax on the mega-wealthy was an attempt to steal the left's clothes and ditch his "president of the rich" label. But it was attacked by the Socialists as a smokescreen to mask an unfair tax system which affords the rich tax breaks and loopholes while everyday people face new taxes on items such as fizzy drinks, cigarettes and visits to theme parks.

The Socialists are aiming to convince France that a caring, sharing left can maintain a strong welfare state while kick-starting growth, cutting debt and creating jobs.

For the first time, the Socialists are holding an open primary race allowing not just party members but the whole electorate to choose the candidate. The 9 October vote is open to anyone on the electoral register if they sign a declaration that they adhere to the values of the left and pay one euro.

Many party members said the Socialist lead in the polls was down to the left-leaning spirit of French society – with the republican ideals of the strong state, social welfare protection and a general anti-capitalist feeling. Often opinion polls favour the left long before an election, but then voters swing right on concrete policy issues at the ballot box.

"The French have their hearts on their left and wallets on their right," said one Socialist activist from the south. "The individualism of Sarkozyism is winning out and our challenge is to convince people we can create a reasonable society where economic development is for everyone not just about a privileged few."