Sarkozy and Merkel kick off week of euro crisis talks
They will take their ideas to an EU summit on Friday that is being seen as crucial for the single currency.
Germany favours strict EU central control while France wishes to preserve more national sovereignty.
Meanwhile, two badly-hit eurozone countries, Italy and Ireland, are preparing tighter austerity measures.
In Italy, Prime Minister Mario Monti is due to seek approval for his government's plans in parliament.
Taxes on the assets of the wealthy will go up, as will pension ages. There will be a major drive to tackle tax evasion.
The severity of the pension reforms caused Welfare Minister Elsa Fornero to break down in tears as she was outlining them on Sunday, saying they had taken a "psychological toll" on her.
Meanwhile Irish Prime Minister Enda Kenny has said the population must prepare for a tough budget this week.
Public spending will be cut by 2.2bn euros (£1.9bn) a year and taxes raised by 1.5bn euros, with VAT increasing to 23%.
Treaty talk
Monday's Franco-German meeting in Paris kicks off a week of meetings involving European leaders, the European Central Bank (ECB) and US Treasury Secretary Timothy Geithner, culminating in Brussels on Friday with an EU summit.
With financial markets putting pressure on some of the eurozone's largest - and most highly indebted - nations, Mr Sarkozy said the stakes were high.
"What will remain of Europe if the euro disappears?" he asked. "Nothing."
France and Germany must play a key role to ensure "a zone of stability", he said last week; Kazinform cites BBC.
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