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These two women battle it out for Paris

Will the French socialists lose control of Paris?

As a second round of the local elections looms in France, the French socialist government is prepared for more losses - and there's even a small chance it could also lose its grip on Paris.

Whatever the outcome of Sunday's vote, for the first time in its history, the French capital will be led by a woman – either the ruling Socialist Party's (PS) Anne Hidalgo, or center-right UMP's Nathalie Kosciusko-Morizet (NKM).

(Read more: Hollande braces for losses in French local vote)

Voting explained

The socialists were largely expected to lose out to UMP party in last weekend's first round of voting, which see 36,000 mayors elected across the country. But the wake-up call was harsher than anticipated, with abstention reaching a record high and the far-right National Front achieving a massive power-grab.

PS even lost out in the first stage of its battle to retain control over the capital. Despite every poll released ahead of the first round indicating that Hidalgo would take the lead, NKM grabbed 35.64 percent of votes - while Hidalgo trailed behind with 34.40 percent.

Paris municipal elections are unique in France as voters do not vote to elect a mayor for the city. Instead, they elect their district's – or arrondissement's - mayor and councillors, from which Paris councillors are elected – and the Council of Paris then choose the mayor.

Nathalie Kosciusko-Morizet and Anne Hidalgo
Joel Saget | AFP | Getty Images

Anne Hidalgo

The capital is one of the left's stronghold, and 54-year-old Hidalgo certainly knows her way around the town hall's corridors. She became the city's first deputy mayor in 2001, under current mayor Bertrand Delanoé.

And although PS lost the first battle – it is unlikely to lose the war, according to Thomas Guénolé, political scientist at Sciences Po university in Paris.

"The left is in a position of strength to win Paris," he said.

The environmentalist left-wing party, Les Verts, came third in the first round of voting, with 8.86 percent of votes. Guénolé explained that many of these voters will switch to PS in the second round, adding: "When you addition the Socialist score to the environmentalist one, Hidalgo has won."

Antonio Barroso, senior vice president at political risk consultancy Teneo Intelligence, agreed that Hidalgo should win – but stressed the margin will depend on her performance within swing districts. The 12th and 14th arrondissements are the main swing districts, and Hidalgo is better placed in both.

"It will be tight," he added.

For Guénolé, Hidalgo's victory will come at a small price. She is unlikely to enjoy the majority her predecessor Delanoé had, and her council will have a larger proportion of Verts, he said.

"It amounts to electing Delanoé for a third time," he added.

(Read more: French unemployment dips – along with confidence)

Nathalie Kosciusko-Morizet

On the only side of the political divide, 41-year-old NKM's journey to the Paris elections has been less clear-cut than her adversary.

NKM occupied several positions in the Sarkozy government, culminating in a position as Ecology Minister in 2010. And while Anne Hidalgo was the PS's only candidate, NKM had to fight off competition and division within the UMP party to run for mayor.

However, despite her surprise lead in the first round of voting, she is still considered the underdog of these elections. NKM is running in the 14th district – but is unlikely to come out on top even here, as the PS is leading in the area.

Economy dominates

Despite their political differences, both candidates have centered their campaigns around the economy, housing, the environment and security.

For both Guénolé and Barroso, NKM's plans were a little less clear than her rival's, especially on housing.

"The electoral campaigns, for both the right and the left, were equal in their inanity," says Guénolé, with both candidates preferring to throw barbs at each other rather than focus on policy.

A debate organised by French broadcasters iTélé and RTL between the two candidates on March 26 was a perfect example of this, he added.

"Nathalie Kosciusko-Morizet kept attacking Anne Hidalgo on Delanoé's legacy, and Anne Hidalgo dropped - every five minutes - that NKM wants to use Paris as a springboard for the presidency," Barroso said.

Girl power?

But despite both mayoral candidates being female, some have argued that this apparent gender equality is not representative of France more broadly.

"It's the tree that hides the forest because only 15 percent of mayors across France are female," Guénolé said, adding that, "on this level, France, its public opinion and elites, have yet to grasp the severity of the segregation against women."

Teneo's Barroso, however, did stress that many women have been district mayors in France, and that some big cities are in female hands.

But he added: "It will send a message to the political establishment that a woman can be the mayor of the most important city in France… (This is) huge because France is a highly centralized country."

(Read more: Hollande meets Obama for a...tea party?)

While the PS is likely to keep control of some of the country's biggest cities - including Paris, Lyon and Lille - the poor results from the first round of voting were irrefutable.

Saddled with the lowest popularity ratings a French president has ever had, Francois Hollande is widely expected to announce a cabinet reshuffle in the days following the second round of the local elections.