The European Commission says it is worried by opinion polls that suggest French voters will reject the EU's constitution in a referendum on 29 May.
Campaigns for and against the constitution are in full swing
The latest poll suggests that more than 60% of French adults would vote against the text - the highest level of opposition in an opinion poll yet.
"The European Commission is worried by the turn of the statistics," said spokeswoman Francoise Le Bail.
Rejection by France would scupper the constitution.
The constitution is meant to ease decision-making in the expanded EU, and needs to be ratified by all EU member states.
The results of the poll for the Metro newspaper, conducted by MarketTools on 20 April, suggest an increase in the No vote, up from 58% in a poll for L'Express released on Thursday. No margin of error was given.
"Of course, there are a number of weeks to go before the referendum. But we very much hope that the figures will change," Ms Le Bail said.
A poll released on Wednesday had suggested the No vote was wavering, placing it at 52%.
However, the campaign against the constitution has steadily won votes amid growing discontent with high and rising unemployment in France.
Trade union are threatening strike action on 16 May in the run-up to the referendum over government plans to scrap a public holiday.
A survey by pollsters CSA for Le Parisien suggested 66% of people opposed cancelling the Pentecost holiday. The government says it needs French people to work on 16 May in order to generate more tax revenues.
Correspondents say voters worry that the EU constitution might undermine France's traditional concern for social issues.
However, the president has tried to convince voters that the referendum should not be seen as a vote of confidence in his government.
In a televised address last week, Mr Chirac warned that France risked being exiled from the political heart of Europe if its people rejected the constitution.