The French government has warned of "humiliation" for the nation if, as polls suggest, voters reject the EU constitution in a referendum on 29 May.
"If we want a submissive, dominated France, a No vote will pave the way for that," Interior Minister Dominique de Villepin told French radio.
Two recent French opinion polls suggest that the No camp will triumph.
EU Commission chief Jose Manuel Barroso has said the French government should explain the constitution to voters.
Duty to explain
He said people were confused about the constitution and the EU directive on services, a proposal to liberalise services across the EU which has aroused concern particularly in France and Germany.
"I hope French politicians can contribute to clearing up this misunderstanding," Mr Barroso said on Monday.
"What the French are going to vote on in this referendum is not the directive on services... It is up to French politicians to explain this."
Mr de Villepin warned that if the No camp won the referendum, France would be "in a corner, reduced to a minor role... It will be a humiliated France".
A No vote would result in globalisation "without any constraints," he said, and Europe would then become "the big market that the Anglo-Saxons dream about, a Europe under US influence, a Europe under Chinese influence".
The constitution project - a wide-ranging blueprint to streamline the enlarged EU's institutions - was spearheaded by former French President Valery Giscard d'Estaing.
Call for action
A French government spokesman warned on Tuesday that "we have to get moving, because we will not get very far by just watching opinion polls that show the No vote effectively rising".
"To get over the hurdle of the No supporters we have to go out onto their territory, debate with them, tackle their arguments and refute them," said spokesman Jean-Francois Cope, quoted by Reuters news agency.
The No campaigners also say the new constitution will pave the way for Turkish accession to full EU membership - something most French people strongly oppose.
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