The meeting is part of a flurry of weekend activity which will also see Mr Sarkozy visit Berlin for talks with German Chancellor Angela Merkel.
They will discuss how to help banks over-exposed to sovereign debt.
The European Commission has urged member states to draft a bailout plan to restore confidence in banking.
However, Germany and France, the eurozone's dominant economic powers, have yet to agree on the way to proceed.
On Friday, the international ratings agency Fitch downgraded the sovereign credit ratings of Italy and Spain, putting new pressure on two of the eurozone's biggest economies.
Another agency, Moody's, downgraded 12 banks in the UK and nine in Portugal.
Plans to expand the eurozone's bailout fund, and give it greater powers, were agreed in July and have been ratified by most national parliaments.
However, these plans are now seen as inadequate. Further action is now being discussed and leaders have said they hope to announce new measures at a G20 meeting in Cannes at the beginning of November.
Downgrades Ms Lagarde, Mr Sarkozy's finance minister until she joined the IMF this year, arrived at the presidential palace in the French capital.
Earlier, a German source told Reuters news agency Paris wanted to be able to tap the eurozone's bailout fund itself to recapitalise its own banks, which have the largest exposure to peripheral eurozone debt.
However, Mrs Merkel said on Friday that the European Financial Stability Facility was a backstop to be used "only if that country is unable to cope on its own".
Fitch cut Italy's rating by one notch, from AA- to A+, following a Moody's downgrade earlier this week.
Fitch cited the "intensification" of the eurozone debt crisis that "constitutes a significant financial and economic shock which has weakened Italy's sovereign risk profile".
The agency also cut Spain's rating by two notches, to AA-.
The ratings agency raised concerns about the strength of Italian banks, particularly in light of the current debt crisis.
It talked of the "small but no longer negligible risk that a further worsening of the eurozone debt crisis and volatility in the value of Italian government bonds will further erode confidence in the banking system".
The agency said a "vicious cycle" could emerge where a growing lack of confidence in Italian banks could knock confidence in government debt, which could in turn undermine the banks further.
With regards to Spain, Fitch also cited the deepening debt crisis, and raised questions about the country's ability to cut its debt levels quickly - and its growth prospects.
The country's high underlying budget deficit and its fragile economic recovery made Spain "especially vulnerable" to external shocks, it said.
Fitch added that it expected growth to remain subdued between now and 2015, and unemployment to remain high. Spain has the highest jobless rate in the eurozone, at more than 20%.
However, the agency said the Spanish economy should grow faster than the eurozone average after this date.
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