Actually, the EU constitution was rejected largely because it was seen as a threat to the welfare state in France. The Left in France was stronlgy against the EU constitution.
That's not the way the news is reading, so perhaps you have different sources.
I think its clear that the French citizens are finally waking up to the fact that it is an undemocratic totalitarianism which they are being asked to impose on themselves. The only place it was popular was in Paris and Brest.