No ballots will be cast in mainland France until Sunday, but voting began Saturday in French Polynesia and French Guiana and on France's islands in the Caribbean and North Atlantic, Guadeloupe, Martinique, St. Pierre and Miquelon.
Opinion polls predict defeat for the constitution, despite a strong campaign for ratification by President Jacques Chirac.
Opponents say a "no" vote will force the EU to revise the charter and make it more appealing to the French and to citizens of the other original members of the European alliance. Supporters say a negative vote will kill the constitution and diminish French influence in Europe.
The constitution does not take effect until all 25 EU member states give their approval. Nine nations have previously ratified the document, either by referendum or parliamentary vote.
Some information for this report provided by AP and Reuters.