Just a few weeks ago François Hollande – then still a candidate vying to become the president of France – wrote a letter to one of the country's leading women's organisations. "The struggle for equality, for women's rights … is not a 'women's matter', but the struggle of every citizen," he said.

The pitch for the female – and feminist – vote became a feature of Hollande's ultimately successful presidential campaign. Among his overtures were the promise of equal representation of women in parliament, to reinstate the ministry of women's rights and to support a new law against sexual harassment.

But French women have heard all this before, notably from Nicolas Sarkozy, who promised equal representation of women in his government when he came to power in 2007. And with the shadow of Dominique Strauss-Kahn – a man accused of sexual assault, sexual harassment and "procuring" women for parties – hanging over his Socialist party, can Hollande really position himself as the first feminist president of France?

He has vocal supporters. During his campaign, a collection of 150 feminists – traditionally, though not solely, aligned with the left — signed a petition supporting his bid to become the next president of the republic. Thalia Breton, spokeswoman for campaign group Osez La Féminisme, said that Hollande had "engaged positively" with the debate, particularly on the creation of a ministry for women and domestic violence. "There are holes in his project and he could go further, but certainly we have far more chance of advancing the equality of women with François Hollande at the helm than Nicolas Sarkozy," she said.

There is undeniably room for progress. The pay gap between men and women in France stands at a reported 19% (compared with 17% in the UK) and 80% of workers earning the minimum wage are women. Despite the fact that fines are imposed on political parties that do not field equal numbers of male and female candidates, female MPs make up only 18.5% of the French parliament, compared with 21% in the UK, 33% in Germany and 46% in Sweden.

When Sarkozy came to power, he promised a rebalancing of power in parliament and appointed women such as Christine Lagarde as France's first female finance minister and Michèle Alliot-Marie as minister of the interior and later foreign affairs. But as his tenure progressed the number of women in his government dwindled, and when he observed a little wistfully in the final gasps of the presidential campaign, "A woman's life is more difficult than a man's because she has three lives: a mother's life, a working life, and a sentimental life," he seemed woefully out of touch.

Can Hollande show more commitment to keeping women in key positions and increasing their number? The early signs are positive. His ex-wife, Ségolène Royal, who lost the 2007 presidential campaign to Sarkozy, could become the first female speaker of the French parliament. Martine Aubry is widely tipped for a key post, although perhaps not France's second female prime minister, while Aurélie Filippetti, a former ecologist and MP in Lorraine, and adviser Fleur Pellerin, a state auditor born in South Korea, look set to take up important roles. The new president's personal life also suggests he has no issue with strong women – his ex-partner Royal attempted to become the first female president of France, while his current partner, Valerie Trierweiler, is a well-respected magazine journalist who has vowed to keep on working after becoming France's first lady.

Rainbow Murray, an expert in gender and French politics at Queen Mary, University of London, believes Hollande's victory could mark a seismic shift for women in France. "He wanted to win women's votes, of course, but I think we will see a big rise in the number of female candidates not just selected, but put in winnable seats," she says.

This is partly because Hollande is desperate to detoxify the Socialist brand after the DSK affair. "The story will die down but it has left an unpleasant taste in the mouth," says Murray. "Hollande will have to make it clear that there is a world of difference between DSK and him, and that he is much better for the women of France."

It is this that may bring genuine progress. Hollande has already mooted the idea of removing state funding from parties that do not adhere to the parity rule, rather than just imposing ineffectual fines. Plans to reinstate the women's ministry are already well developed.

Women's groups are also ready to hold him to account. "Whenever a president comes into power we get promises, but now we are looking for something concrete," said Wassila Ltaief, secretary general of French feminist movement Ni Putes, Ni Soumises. "The fight continues."