At the meeting, Sarkozy declared that he was dropping a proposal for a new secretariat for the 16 EU members that use the euro. Merkel was opposed to this not including all 27 members of the EU.
Sarkozy also came round to agreement on Germany's proposal to withdraw rights of EU members who are in serious breach of the bloc's rules on deficits.
But he said that eurozone leaders would still hold what he called "operational, pragmatic and rapid" meetings if the need arose.
The two European leaders also agreed to push for a financial transaction tax and a global banking levy at the G20 summit in Toronto, Canada later this month.