Although I'm not keen on the EU Constitution in its present form, I agree that the EU should have a constitution.
The next step should be to recognize that every paragraph added to the Constitution makes more people fail to read it, fail to understand it, or fail to agree with it.
Therefore, whoever is responsible for the document in future should look at every paragraph in it and ask, "Is this paragraph vital for the future of the EU?" If not, take it out.
The resulting minimal document can then be resubmitted to the people of Europe with more hope of success.
It's perhaps unlikely that any conceivable Constitution would be approved by every EU country. Therefore, it's necessary to plan ahead and stipulate how to proceed with a Constitution without unanimous agreement. The obvious method is to say in advance that, if a large majority of Europeans approve the Constitution, any dissenting countries will be required to accept it or leave the EU.
If this seems too drastic, perhaps dissenting countries could be offered some kind of associate membership of the EU. But this status would be awkward to define, and would presumably have to be defined in the Constitution itself (an unwelcome complication).