France holds a referendum on the issue on 29 May. If French voters defeat the ratification of the referendum, it is effectively dead, since unanimity among member states is required.
The Ligue has participated in a broad front campaign against the constitution, which has included the French Communist Party, ATTAC France and others.
Opposition to the constitution remains high, with opinion polls showing more than 50% intending to vote ’no’. This is despite the partial (and probably temporary) withdrawal of most measures in the so-called ’Bolkestein directive’,  which would have imposed the compulsory opening up of services in all EU member states to foreign bids and competition. National governments would no longer be able to impose strict conditions on providers of public utilities and other services, or take any measures to protect either workers or consumers.
The deferment of most of the Bolkestein provisions was caused by pressure from the French government, following massive popular protests. Chirac calculated that he was sure to lose the constitution referendum if Bolkestein remained intact.
Nevertheless, the Ligue, and indeed most leftwing opponents of the constitution, see its lengthy and detailed requirements of member states as an instrument providing for the thorough neoliberalisation of every aspect of te European economies, irrespective of the immediate fate of Bolkestein.