A second electoral defeat for the document - by another founding member of the European Union - would make it tougher for EU decision-makers in Brussels to ignore public opposition, analysts say.
As many as 12.7 million voters will be eligible to take part in the 1 June vote, the first referendum in the Netherlands.
Most of the 25 EU countries are leaving it to their parliaments to decide on ratification, where the outcome is likely to be straightforward.
But six more countries have scheduled referendums - Spain already has voted yes - among them Britain. Prime Minister Tony Blair said the French vote called for a pause for reflection, and he will be looking to the outcome in the Netherlands when deciding on putting the issue to the British people.
A failure to win approval here also would put the ruling government of Prime Minister Jan Peter Balkenende, already at a record low in approval ratings, at loggerheads with a majority of the Dutch people.
A no-vote would be a setback for
Dutch PM Balkenende (L)
Balkenende's party said on Monday it will accept a negative verdict from the people as long as the turnout reaches 30% and 55% of the population votes no.
Pollsters and political analysts said the French result will likely further motivate the 'no' camp in the Netherlands and discourage supporters from taking part.
Polls have for weeks indicated the Dutch will reject the draft, although the yes vote has made small gains over the past week.
Eddy Habben Jansen, deputy head of the nonpartisan Centre for Political Participation, said the French rejection will "clearly increase the chance of a Dutch no. There will be less restraint to vote no over fears that the Netherlands will isolate itself".
Out of 85,000 participants in an internet poll over recent weeks, 56% have said they will vote no and 44% yes, Jansen said. There was no margin of error for the poll, taken on a web site visited by more than half a million potential voters.
A second internet poll by pollster Maurice de Hond published on Saturday showed 57% of the Dutch oppose the constitution, versus 43% in favor, with others undecided.
The 'no' camp brings together an unusual and diverse alliance of liberals, concerned that greater power for Europe could lead to an erosion of Dutch social policies like tolerance for euthanasia and marijuana, and hardliners concerned the Dutch would lose control over immigration policy.
Mendeltje van Keulen, a researcher at the Dutch Clingendael Institute for International Relations, expects the British government will scrap plans to hold a referendum in the case of a second defeat of the charter in the Netherlands.
"A no vote here would send a clear message to EU leaders that the gap between the voters and the politicians has only grown in recent years, despite attempts to close it"
Mendeltje van Keulen,
Dutch Clingendael Institute for International Relations
"A no vote here would send a clear message to EU leaders that the gap between the voters and the politicians has only grown in recent years, despite attempts to close it," Van Keulen said in an interview. "It will also show how little confidence there is in the current Dutch government."
With all indicators showing the Dutch will follow the French, the 'yes' camp continued intense campaigning on Monday. Left-wing opposition leaders and government ministers launched a last ditch media offensive to sway their constituents to support the historic document.
The constitution - more than two years in the making - is meant to further a 50-year process of bringing together nations and peoples divided by centuries of war. It needs the backing of all 25 members to take effect in November 2006. Nine countries have already ratified it.