Britain has the Pitcairn islands and the Dutch have West Indian Curaçao, but these cannot compete with the impressive French portfolio of dominions around the globe from the Pacific to the Amazon jungle.

Their 1.4m voters could swing the result in the closely fought May 29 French referendum on the European Union’s constitution and determine the future of Europe, not to mention influence the timing of Tony Blair’s departure from No 10.

The Wayampi do not know him but excitement was building last week at the prospect of playing their part in the politics of the palan isi lena, or the “land of the white man”, as Europe is known.

Many speak only rudimentary French and have little understanding of qualified majority voting, but an election is always a welcome occasion for a gathering in this alligator-infested corner of French Guiana in South America.

They will watch Joseph Chanel, their leader, in fascination as he slips a red, white and blue French mayoral sash over his tribal tunic to supervise voting. Copies of the constitution, shipped at considerable expense on Air France from Paris, and then by helicopter and canoe up the river from Cayenne, the distant capital, will come in handy for wrapping tapir meat and lighting fires.

“We are European citizens,” said Chanel, a renowned Wayampi hunter, on a visit to Cayenne. “It is an obligation for us Wayampi to vote.”

In Cayenne, a rickety town by the sea, they drive Citroëns and visit internet cafes. Civilisation has gradually taken root since the brutal days of the former French penal colony depicted in the book and film Papillon.

But how free and fair an election will they hold in the Amazon? Or, for that matter, in the Wallis and Futuna islands in the Pacific, where three kings rule by fiat? So narrow was the victory of the “yes” camp — 540,000 votes — in the 1992 referendum on the Maastricht Treaty, which paved the way for the euro, that it prompted unsubstantiated rumours of skulduggery in the “Dom Toms”, as the overseas “departments” and “territories” are known. Suspicions arose partly because the “yes” vote there averaged 70%, far higher than in France.

This time it could be just as close. According to the latest opinion poll, to be published tomorrow, 53% of France will vote “no” and 47% “yes”. In regions such as French Polynesia, where irregularities caused an election to be suspended last year, there is every reason to wonder if desperation might drive either side to cheat.

Similar concerns are felt in Corsica, where popular belief has it that “even the dead are made to vote”.

The Wayampi, for their part, seemed ill-equipped to weigh all the issues. Although Chanel said he would never tell people whom to vote for, he added that “I like to stress the benefits Europe has brought us”.

Not that they need reminding. The Wayampi are among the most pampered “Europeans” anywhere. Their new landing stage on the river Oyapock was paid for by Brussels. The EU also funded the school in Comapi, whose big moment was a visit in 1997 from President Jacques Chirac to inaugurate the local dirt airstrip.

Chirac no doubt wishes the unpredictable French could be more like the Wayampi. They are expected to turn out in big numbers to vote “yes”.

In a previous election, when the turnout reached only 74%, it was considered a disaster. “I let them know,” said Serge Casala, the deputy Wayampi leader, “that I was really not happy about that.”

Not all French overseas subjects are as content to be consulted as the Wayampi, however. In Mayotte, an island in the Indian Ocean, there was widespread indifference on the subject of Europe, and only 8% of the inhabitants voted in the Maastricht referendum.

In Guadeloupe and Martinique in the Caribbean, just 20% bothered to turn out in 1992. The turnout was only marginally better on the island of Réunion, despite its image of itself as “a European aircraft carrier” in the Indian ocean.

In the hope of encouraging a better result this time, the EU recently approved an annual, free air fare to Paris for students from the Dom Toms attending universities in France. It also rushed through an extra £16m in structural aid in April to West Indian banana growers, many of whom come from the French islands.

Luminaries of the “yes” campaign have been dispatched to the Dom Toms, among them Dominique Strauss-Kahn, the former socialist finance minister, who warned that the region could become the “Florida of the referendum”, a reference to President George W Bush’s election victory in 2000, which depended on a few hundred votes from the state of Florida.

Yesterday it was Chirac’s turn to sound the alarm. In a television message to the Dom Toms, broadcast from the Elysée Palace, he reminded voters how much they benefit from EU money: Guadeloupe, Martinique, French Guiana and La Réunion received £2.2 billion in aid between 2000 and 2006 and the £34m received by French Guiana in the past year amounts to about £650 a voter.

Chirac’s loss of influence at home, however, has been mirrored by a waning of support in the Dom Toms where allies, including Gaston Flosse, the French Polynesian leader — who made Chirac godfather to one of his children — have recently been driven from power.

Whatever the result of the voting, the Wayampi, at least, will enjoy it.

On election day, they usually line up outside the polling station long before it has opened. Coming of age these days does not involve slaying an alligator: Chanel, the mayor, is in the habit of telling first-time voters as they emerge from the polling booth: “Now you’re a man.”

Additional reporting: Nicolas Ransom, Cayenne

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