Updated

Neck-and-neck in the polls just one week before the election, France's leading presidential candidates rallied tens of thousands to separate events Sunday to outline two very different visions of the future.

On the iconic Place de la Concorde in the posh western side of Paris, President Nicolas Sarkozy appealed to his supporters' patriotism, invoking France's history and the names of past leaders like Napoleon and Charles de Gaulle. Painting a picture of a country that suffers without complaint, the conservative played up his own leadership experience as vital to confront an economic crisis and to maintain France's global status.

On the edges of Paris' working-class east, Socialist contender Francois Hollande told supporters that France needed nothing short of a top-to-bottom change. In a dig at Sarkozy, who has been seen as too close to the rich and too fond of free-market economics, Hollande promised to be a president "stronger than the markets, stronger than finance."

While most polls show the first round on April 22 is too close to call, they have Hollande ahead in the decisive May 6 runoff.

Sarkozy has dismissed such polling in recent weeks, and did again on Sunday. He began his speech by joking — "They thought you wouldn't come!" — but his message and tone seemed clearly aimed at rallying troops for a tough battle.

He promised to take the necessary measures to create a state that "rejects the drug of public expenditure," a reference to his commitment to balance the country's budget by 2016.

He hailed the reforms his government had made as protecting France from the worst of the global recession and the European debt crisis, but insisted now was not the time to give up the fight — and an experienced leader was needed to continue it.

Hollande, for his part, nearly shouted himself hoarse in hammering home his message of the need for change.

"Why continue what has failed? Why continue going in the wrong direction? We must turn the page," Hollande said. "France is not bankrupt, it is its leaders who are bankrupt."

He promised again to renegotiate a European treaty designed to limit government overspending to include pro-growth policies and to ensure that wealth is distributed more fairly.

The economy is a major issue, especially as unemployment pushes 10 percent. Both candidates have promised to drastically cut the country's sizable deficit in the next few years, even though growth is forecast to be just 0.7 percent this year.

But a killing spree in March by a man police described as an Islamist militant has also brought security and concerns about Muslim integration to the forefront of the campaigns.

And even as the two men battle one another, each is also fighting off the fringes of the political spectrum.

Hollande is nervously eyeing far-left candidate Jean-Luc Melenchon, who has electrified crowds by calling for a new revolution and more rights for workers. Sarkozy is trying to peel votes away from far-right candidate Marine Le Pen, who has railed against immigration.

Both Sarkozy and Hollande are encouraging their supporters not to wait for the second round to vote for them. In such a close race, each is looking for any advantage, and momentum going into round two could be a decisive factor.

Supporters at both rallies were completely convinced their man would win.

Hollande "doesn't have the charisma of a president," said Elodie Benamou, a 25-year-old physical therapist.

But Francoise Bricquet said only the Socialist sees things as they are.

"For five years, the real problems of real people have been ignored," said the 57-year-old. "There are a lot of people who want that to change."

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Associated Press writers Sylvie Corbet and Cecile Brisson contributed to this report.