French voters' clear "No" to the EU constitution has left European leaders struggling to define the way forward.
The "No" camp on both the right and the left is jubilant
European Commission President Jose Manuel Barroso said there was now "a very serious problem" and there was no willingness to reopen negotiations.
In the French referendum almost 55% of people voted "No", with 45% in favour. Turnout was high, at about 70%.
It is a severe - perhaps fatal - blow to the EU constitution, which needs to be ratified by all 25 member states.
French President Jacques Chirac accepted the voters' "sovereign decision" on Sunday, but said it created "a difficult context for the defence of our interests in Europe". He had campaigned hard for a "Yes" vote.
Mr Chirac will address the nation on television on Tuesday and make an announcement about the French government, his office said.
Correspondents say it is widely expected that Prime Minister Jean-Pierre Raffarin will step down.
The next big test for the EU comes in the Netherlands on Wednesday, when the Dutch vote in a referendum - and the "No" camp has a clear lead in the opinion polls.
UK Prime Minister Tony Blair - whose government will take over the EU presidency on 1 July - called for "time for reflection". France's rejection of the constitution raised profound questions about Europe's future, he said.
The BBC's world affairs analyst Paul Reynolds says there is no Plan B for the EU and no clear way forward, with moves towards further integration now in doubt.
Struggle for unity
The constitution was finalised last year after long negotiations among EU governments. Its aim is to streamline EU institutions following the admission of 10 new members last year.
Member states can ratify the constitution through a referendum or by parliamentary vote. So far, nine countries have formally endorsed it and eight national referendums are still to come.
European Union foreign policy chief Javier Solana insisted that the EU's international role must not suffer and warned Europeans against entering "a zone of paralysis psychologically".
The president of the European Parliament, Josep Borell, also put a brave face on the result, saying "I think we have to continue, asking the other countries" and "we should not stop the process" of ratification.
France in turmoil
Late on Sunday, jubilant "No" supporters gathered at the Place de la Bastille in Paris - where the French Revolution began - chanting "we won" and sounding horns.
ALREADY RATIFIED TREATY
Those who rejected the treaty came from across the political spectrum, including Communists, dissident socialists and right-wing parties.
One of the leading right-wing opponents of the treaty, Philippe de Villiers, said: "Europe has to be rebuilt. The constitution is no more."
He urged Mr Chirac either to stand down or dissolve parliament.
The leader of opposition Socialist party Francois Hollande, from the "Yes" campaign, voiced "regret" over the result, but blamed Prime Minister Jean-Pierre Raffarin.
Dutch Prime Minister Jan Peter Balkenende urged his nation to approve the treaty despite France's rejection.
"There is all the more reason to say 'Yes' so that some progress can be recorded," he said.