Despite the misadventures of Dominique Strauss-Kahn, hopes are high in France’s Socialist Party as its voters go to the polls on Sunday to choose a candidate for next year’s presidential election to run against centre-right incumbent Nicolas Sarkozy.

Sarkozy is certainly not an opponent to take for granted, and his record in government is by no means discreditable. But with no end in sight to the European debt crisis, governments across the EU are looking vulnerable and the Socialist standard-bearer — almost certain to be former party secretary François Hollande — looks like starting as the favourite.

In June and July the polls were close, but since then Hollande has drawn away. The most recent Ipsos poll of likely voters puts him at 44%, well clear of current secretary Martine Aubry on 27% and 2007 candidate Ségolène Royal on 13%; his support is also more solid than theirs. The final candidates’ debate this week seems unlikely to have changed much.

The Hollande camp is now under fire for overconfidence; while Wednesday’s debate was still in progress, his campaign manager Pierre Moscovici tweeted “Les jeux sont faits” — which could be translated as “Game over”. But barring some disaster in the last 48 hours, the only question seems to be whether a runoff the following week will be required or whether Hollande can win a majority in the first round.

For the 57-year-old Hollande, it’s been an interesting journey to this point. He took the job of party secretary in 1997, when the Socialists were in government, and became the party’s leading spokesperson on its move into opposition in 2002. He was regarded as a front runner for the presidential nomination in 2007, but it was his partner, Royal, who captured the party’s imagination and was a runaway victor in the primary, before losing to Sarkozy.

Hollande and Royal separated before the campaign, although it only later became public, and the tension between them has added to the soap-opera atmosphere of the contest this year. Royal, however, has failed to reach anything like her earlier heights, while Aubry, who narrowly defeated Royal in a bitter contest for the secretaryship in 2008, has not done much better.

Hollande’s problem is that he is seen as dull; he is widely respected but attracts little real enthusiasm. There are worse reputations to have than dullness, as Strauss-Kahn discovered, but it has many in the Socialist Party looking forward to generational change. The two youngest primary candidates, Arnaud Montebourg (48) and Manuel Valls (49), although still well back, have both made up significant ground as a result of the debates.

This week’s Economist notes mischievously that the Socialists are “not famed for bold modernity”: traditionally the party is run by a small number of oligarchs, known as the “elephants”. Royal’s populist campaign last time was a break with tradition, and Sunday’s open primary, where all left-leaning voters are eligible to participate, is another step forward.

When a party is reforming (or trying to), it’s often a matter of perspective whether someone is part of the solution or part of the problem. Ten years ago, Hollande was a young turk leading the drive for modernisation; now he is the establishment personified. But if he can go on to beat Sarkozy, his party will forgive him almost anything.