Can Paris's next mayor - whoever she is - revitalize the city?

Ernest Hemingway once wrote: "If you are lucky enough to have lived in Paris as a young man, then wherever you go for the rest of your life, it stays with you, for Paris is a moveable feast." And indeed, Paris has long been at the cutting edge of art, literature, and music, and drew creative masters from around the globe. The city is still one of the world's most popular for tourists, who revel in the patrimony that’s been so lovingly preserved.

Today, however, the so-called “museum city” has lost some of its cache, as many young Parisians are moving abroad for better wages and more opportunities, and Barcelona and Berlin are stealing the cultural thunder.

But the two candidates vying to become the mayor of Paris in the second round of municipal elections this Sunday hope to bring some verve back.

The winner will make history no matter what: for the first time Paris will have a woman at its head. Facing off are Anne Hidalgo, a Socialist, and center-right Nathalie Kosciusko-Morizet, known by her initials NKM.

While that's a point for modernity (not to mention a point for French women, who need it), Paris's role in the 21st century has been a reoccurring theme in the race, says Madani Cheurfa, an expert on French politics at SciencesPo.

Amid a general perception that Paris lacks the energy and dynamism of Berlin or London, he says, these women have sought to project themselves as symbols of “what is a Parisian, and what is Paris, a city capable of competing with all the cities in the world of globalization in 2014.”

Finding Parisian relevance

At meetings with the Anglo-American Press Association of Paris, both women focused on their plans to maintain – or create – Paris’s relevance in Europe today. Ms. Hidalgo, who has been the deputy of Paris Mayor Bertrand Delanoë for 13 years and is the daughter of Spanish immigrants, spent much of her time listing Paris’s strengths over London’s. (That was in part, admittedly, because of the Anglo influences in the questions of the audience.)

She ultimately called London a “suburb of Paris,” garnering not a few laughs, and said Paris was friendlier to both start-up and family culture.

NKM, who comes from a well-heeled family and struggles to portray herself as "everyday" as her rival, showed up 20 minutes late, after her team said she ditched the car in a rainstorm and hopped on the metro. Despite the rain, she appeared stylish in all black and lamented a city today that takes more energy than it gives back – a concept that anyone of the yoga-latte set can identify with.

"There's now a whole generation dreaming of living abroad, starting a business in London, being an artist in Berlin," she said.

Most voters in Paris care about affordable housing – of which there is very little in Paris, a main reason that young people opt to live elsewhere – as well as jobs, crime, and pollution. But both women floated some ideas that would add to Paris's cultural portfolio – like creating urban art projects in abandoned tunnels (Hidalgo) or turning unused metro stations into swimming pools and nightclubs (NKM).

Dour national mood

Their run-off Sunday is one of thousands across the country, which follow last Sunday’s first go. The major takeaway from round one was pessimism: high rates of abstention and better-than-expected results for the far-right National Front, mostly explained by discontent with the mainstream parties, especially the ruling Socialists. NKM, in fact, squeaked out a few more votes than Hidalgo, who has been long favored to win.

The dour national mood has been another reoccurring theme in France, even making the front pages of Le Monde recently, after an Ipsos survey showed that 85 percent of respondents believe France is a country in decline.

Mr. Cheurfa says that Paris itself isn’t in decline. It’s still a beautiful, mesmerizing place with a high concentration of foreign companies that still manages to exude a sense of tradition. There are great bike sharing programs and ditto for electric cars, and the Seine turns into a “beachfront” each summer. But compared to Shanghai or London or Berlin, he says “there is a delay in adapting to a globalized world.”

And that’s created an image problem. What a 21st century woman can do to change that reputation is now the factor to watch.