The treaty is intended to streamline EU decision-making following enlargement of the bloc, creating a new EU president and foreign affairs chief.
Other treaty reforms, such as a new voting system and smaller European Commission, are designed to allow for further EU enlargement. The current Nice Treaty was drawn up for an EU of 27 nations.
Critics see the Lisbon Treaty as further evidence of a federalist, pro-integration agenda at work in the EU.
"There will not be any new treaty. It's either Lisbon, or it's Nice," Mr Sarkozy said, drawing strong applause from MEPs.
EU leaders are due to meet in October to hear proposals from Ireland's prime minister about how to move forward after the "No" vote.
"I will go to Ireland on 21 July to listen and talk and try to find solutions," Mr Sarkozy said on Thursday.
"The French presidency will propose a method and, I hope, a solution either in October or in December."
'Family of 27'
He insisted that no country should be left behind in the European project.
"Maybe one day we'll be obliged to have a two-speed Europe, but that will be the last resort… Europe is a family of 27 nations, we can't leave anyone behind. We have to keep everyone together."
He said the EU's acceptance of 10 new members in 2004 - most of them former communist bloc countries - had taken place without the necessary institutional reform.
"I always regretted that Europe was not wise enough to give itself the right institutions before it was enlarged. That was a mistake... I want to say forcefully that we must not make the same mistakes again."
Turning to economic policy, Mr Sarkozy defended his right to comment on matters such as eurozone rates and EU trade policy. He has previously criticised the policy pursued by EU Trade Commissioner Peter Mandelson.
"If we, the political leaders, do not have the courage to debate - what's the right economic strategy, what's the right monetary strategy, or the right exchange rate... no-one has the right to prevent a useful debate.
"We are not calling into question the independence of the ECB (European Central Bank) if we ask whether it is reasonable for interest rates to go up to 4.25% when Americans have 2%," he said.
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