From the BBC:
Strong divisions
The latest polls have provided mixed messages. One suggested support for the "No" campaign had fallen to 52% and another that it was up to 56%.
Parisians share their views on the EU constitution
The campaign has reflected strong divisions between those who say the constitution will ensure France's influence at the heart of Europe and critics who argue it will undermine the country's ability to protect jobs, wages and living conditions.
Both the governing centre-right UMP party and the opposition Socialists have urged voters to support the proposed constitution.
But leading Socialist dissenters joined with Communists and union leaders in Paris on Friday to press for a "No".
The BBC's William Horsley in Paris says the debate has engaged the nation on European issues - including economic policy and immigration - in a way rarely seen before.
He says the result is awaited with both anxiety and anticipation across France and the EU.
For one day, French voters hold the immediate future of the union in their hands, he says.