By Caroline Wyatt
BBC News, Paris
On Tuesday France joined Britain for an international Fleet Review presided over by the Queen, for a celebration of the sea - which also commemorated 200 years since the Battle of Trafalgar.
The defeat at Trafalgar affected France's trust in its navy
It was one of the finest moments in British naval history, but a catastrophic defeat for the French, who lost many ships and thousands of lives.
A re-enactment of a battle will be held between a blue and a red team, rather than Britain versus France, in order not to offend the French.
But how do they see this anniversary?
Britannia may think it rules the waves, but on Tuesday it is a French warship that will dominate the English Channel.
She is the pride of the French navy - the nuclear-powered aircraft carrier, the Charles de Gaulle.
She is 261m (285 yards) long, 64m (70 yards) wide and weighs 42,000 tons - dwarfing all the other vessels taking part in the International Fleet Review.
France is sending a total of six ships to take part in the review, during which a certain battle will be re-enacted.
It may not be called the Battle of Trafalgar, in deference to French and Spanish sensibilities, but few are in any doubt as to which sea-battle is being commemorated: a defeat still remembered with profound sadness by the French Navy.
"For the French navy, it was traumatic - and hugely sad," Vice-Admiral Alain Dumontel of the French Navy tells me, on board the Charles de Gaulle.
"For a long time, it affected the way France perceived its navy, and we lost 10,000 sailors out of 15,000 men as a direct result of the battle and its aftermath.
"But beyond the heroism and our sadness, we've been able to learn more positive lessons from this defeat for today and for the future."
One of the sailors on board the warship jokes that the Charles de Gaulle will be escorted into the English Channel by a British frigate in order to "ward off the spirit of Admiral Nelson", fatally injured by a French sniper during the Battle of Trafalgar.
The British and French navies are the strongest in Europe
Yet the Captain of the Charles de Gaulle, Xavier Magne, says Admiral Nelson is admired by the French navy as well for his tactical skills and his leadership.
Xavier Magne insists he welcomes the chance to show France's largest warship at Tuesday's celebration of the sea, not least to prove just how far Franco-British relations have come over the years.
"We are happy to go and celebrate that with your British forces.
"Trafalgar is the past, and now we are looking to the future together in the European Union, and better defence co-operation within Europe."
Yet even as Britain celebrates the 200th anniversary of Trafalgar, few in France will mark it.
Bruno Ponsonnet is the curator at the Paris Maritime Museum, who last year organised an exhibition called Napoleon and the Sea, yet nothing similar is planned for this year.
"Why should the French talk about Trafalgar?" he smiles, in front of a French painting of the moment Admiral Nelson was shot.
"Trafalgar was a defeat and a few weeks later we had the great victory of Napoleon's forces at Austerlitz, making him the master of continental Europe.
We had so many victories in this era, so why should we talk about Trafalgar? It's a matter for the British people, but not for the French people."
These days, our two navies may no longer be exchanging cannonballs, but our two leaders certainly are, with Jacques Chirac and Tony Blair, firing almost daily broadsides across the Channel.
So is this rivalry a legacy of Trafalgar, and does that historic battle mean anything to ordinary French people today?
"Trafalgar? Course, every Frenchman knows that!" says one French businessman on the Champs Elysees in Paris, in flawless English.
"It was the great victory of Great Britain against Napoleon's vessels. I have been to Trafalgar Square!
"Generally speaking, if you ask any Frenchman in the street about the English people, they consider them friends - whatever happens on the political level."
Europe's naval defence
A French pensioner says he remembers the courage of Britain during World War II, but he believes that the British have always been slightly wary of the continent.
"The British have an insular mentality. They are typical of people living on an island, however big the island."
As the Charles de Gaulle prepares to take its place in the Fleet Review, it certainly seems the French Navy is keen to look to the future, rather than dwell on the battles of the past and to emphasise current and future co-operation with Britain.
Admiral Nelson's skills are admired by the French navy, too
And these days, of course, the French navy is rather larger than the British. French Vice Admiral Alain Dumontel says both sides will use this International Fleet Review as a chance for some naval diplomacy.
"It's good because as history shows there are many navies in Europe, of which two are more important than the others - the Royal navy and the French navy," he smiles.
"We cannot imagine constructing a European naval defence force that is not based on the Franco-British couple.
"Yes, there are things that divide our two nations, but there are many more which bring us together.
I am an optimist and I believe the future of European naval co-operation is Franco-British."