BBC
Mr Sarkozy said a new treaty should be in place by March to ensure such a crisis never happened again.
They said eurozone states should face greater checks on their budgets and sanctions if they ran up deficits.
The Paris talks come ahead of an EU summit on Friday that is being seen as crucial for the future of the single currency.
Mrs Merkel said France and Germany wanted to see "structural changes which go beyond agreements".
The two leaders said they wanted treaty changes to be implemented by all 27 EU member states, but if that was not possible, just the 17 states which have adopted the euro.
"This package shows that we are absolutely determined to keep the euro as a stable currency and as an important contributor to European stability," said Mrs Merkel.
Mr Sarkozy said they wanted a new treaty "to make clear to the peoples of Europe, members of Europe and members of the eurozone, that things cannot continue as they are".
He said they wanted treaty discussions to be negotiated and concluded by March, "because we must move quickly".
Their proposals include:
Mr Sarkozy said things in Europe could not continue as they were
The leaders of France and Germany say the EU needs a new treaty to deal with the eurozone debt crisis.
The statement from French President Nicolas Sarkozy and German Chancellor Angela Merkel came after they held crisis talks in Paris.Mr Sarkozy said a new treaty should be in place by March to ensure such a crisis never happened again.
They said eurozone states should face greater checks on their budgets and sanctions if they ran up deficits.
The Paris talks come ahead of an EU summit on Friday that is being seen as crucial for the future of the single currency.
Mrs Merkel said France and Germany wanted to see "structural changes which go beyond agreements".
The two leaders said they wanted treaty changes to be implemented by all 27 EU member states, but if that was not possible, just the 17 states which have adopted the euro.
"This package shows that we are absolutely determined to keep the euro as a stable currency and as an important contributor to European stability," said Mrs Merkel.
Mr Sarkozy said they wanted a new treaty "to make clear to the peoples of Europe, members of Europe and members of the eurozone, that things cannot continue as they are".
He said they wanted treaty discussions to be negotiated and concluded by March, "because we must move quickly".
Their proposals include:
- automatically applying sanctions to any state which breaks the 3% public deficit rule
- requiring eurozone national budgets to include a "golden rule" against running up deficits, with those budgets to be verified by the European Court of Justice
- no introduction of jointly held euro bonds
- eurozone heads of government to attend a summit every month as long as the crisis persists
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