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.
The treaty was supported by both major political parties - UMP (Union for the Popular Movement) and PS (Socialistic Party). The opposition consisted of both extreme leftist (PCF - French Communist Party, CGT - communist trade union, and the left wing of the PS) and so-called far right (that is Le Pen's National Front and de Villers' Rally for France).
To summarize, the French people did the right thing, but for all the wrong reasons.
We must be reading different news sources. The major complaint from the left--and left in France means socialists and communists--was that the constitution was too liberal. You have to understand that in continental Europe, liberal still retains its original meaning of less government regulation and free markets across national boundaries. In English speaking countries, the word liberal changed to mean the social welfare state.
So when they talk of liberals in France, think of them as pro-business people. The majority of socialists voted against the treaty because for them it was too liberal and Anglo-Saxon, even though liberal doesn't mean pro-business in English-speaking countries any more. Sound confusing? Well, it is.