François Hollande this morning said that France’s Socialists had given him “the large majority that I had asked for”, but in reality his victory in the second round of the primary, although clear, was less impressive than he and the party must have wanted. It’s another signal that next year’s election against Nicolas Sarkozy will be no walkover.

Preliminary results give Hollande 56.6% of the vote against 43.4% for his rival, party secretary Martine Aubry. Aubry quickly conceded defeat, and pledged Hollande her full support: “I will put all my energy and all my strength so that in seven months he will be our next president”.

Hollande led by 39.2% to 30.4% in the first round. That means that of the roughly 30% who voted for one of the other four candidates, fewer than two-thirds of them switched to Hollande, even though three of those candidates had endorsed him and the fourth — Arnaud Montebourg, who was the most left-wing as well as the best performer in the first round — said he would be voting for Hollande, although he avoided a formal endorsement. It’s much less clear-cut than 2006, when Ségolène Royal won with more than 60% in the first round.

Nonetheless, the “open” primary has been seen as a great success. More than 2.7 million people voted, and the Socialists have been buoyed by the display of unity and by poll results that show Hollande beating Sarkozy by margins of up to 60-40. They are well aware, however, that the hard work is just beginning.

These have been lean years for the European left. Since Sarkozy’s victory in 2007, the right have swept to power in Italy (2008), Germany (2009), Britain (2010) and Portugal (2011), and also retained office in Sweden (2010) and Poland (just last month). Even the left’s recent victory in Denmark was more a result of voters shifting from the right to the centre.

Europe’s open-ended economic crisis has certainly fuelled popular discontent, but so far the established parties of the left have been unable to translate it into electoral support. France will be the first big test of whether that pattern is changing. (An early election in Italy before then is quite possible, but Silvio Berlusconi’s position is so idiosyncratic that it would be less useful as an indicator in any case.)

Whether Hollande is the best candidate to be fronting such a test probably depends on what you think the left’s problem has been. If it’s that voters want a safe pair of hands and want to steer away from dangerous radicalism, then you could hardly do better: Hollande is a classic “consensus” politician, steeped in the French establishment, and he promises to be a “normal” president in contrast to the mercurial Sarkozy.

Looked at another way, however, Hollande’s advantages become handicaps.

If voters are tired of business as usual and are looking for something new and different, he is unlikely to provide it. And his pleas for “respect and dialogue” may fall short when matched against Sarkozy’s toughness.

Moreover, voters seem aware that the current crisis is primarily a debt crisis, and that’s enough reason to be sceptical of a Socialist Party that, more than in most countries, has shown an unwillingness to fully break away from its big-spending past. Hollande is off to a good start, but there’s a long way to go.