Even Napoleon's military genius is doubted by some historians. Was Austerlitz won through a great stroke of tactical ingenuity? Or because fog blanketed the battlefield at an awkward moment, leaving the Austrian and Russian armies blundering around in the mist? Napoleon was certainly lucky on the battlefield of Austerlitz but the campaign leading there demonstrated all the brutal, decisive qualities which made him - for 15 years - the supreme figure in Europe.
Napoleon transformed late 18th-century warfare by abandoning the dilettant, aristocratic, almost sporting approach to battles which had gone before. He marched troops rapidly from one place to another over huge distances; he attacked enemies from the rear; he fought battles to destroy the strength of the enemy, not just to win the day.
Thus the Austerlitz campaign, which ended 60 miles east of Vienna in early December, began in Boulogne-sur-Mer, on the Channel in early August.
Napoleon was vaguely planning to invade Britain but could not do so while Nelson ruled the waves. As soon as Britain signed a three-way alliance with Austria and Russia against France, Napoleon ordered the 200,000 troops of the Grand Army to march east to make a pre-emptive attack on the Austrians. A little later, he ordered the French navy out of port in the Mediterranean, more as a diversion than anything else.
By turning his army east, he, in effect, abandoned his plans to invade Britain - hence his judgement that Trafalgar on 21 October, 1805 was an " irrelevance". (In truth, had Nelson lost the battle as well as his life, Britain would have been vulnerable to a post-Austerlitz invasion and 19th-century history would have been rather different).
After a number of skirmishes and smaller battles, Napoleon, with 70,000 men, took on 90,000 Russians and Austrians on the morning of 2 December, 1805.
Within six hours, although they held the best ground, the Russians and Austrians were not only defeated but crushed. More than 20,000 Russian and Austrian soldiers died; another 20,000 were captured. The French lost 9,000 men, killed and wounded.
Napoleon was one of the first masters of PR and propaganda. He wrote the history of the battle himself soon afterwards, insisting he had pre-planned every move.
In truth, the victory at Austerlitz was won partly through the fog of war - in this case, literal fog. Napoleon feinted to retreat, encouraging the Austrians to leave their high ground and try to cut off the French route to Vienna. Heavy mist descended. The Austrians poured down from the plateau they held and French troops poured on to it. By the time the mist lifted, the French dominated the battlefield and chopped up the enemy at will.
Napoleon fought a brilliant battle, adapting to events more rapidly than his enemies. But would his tactics have worked without the fog? His account fails to mention the weather.
The victory placed Napoleon in an utterly dominant position on the European continent. It also went to his head and hastened his end.
The positive, but intelligent, French view of Napoleon is that he turned into a brutal dictator but that the French Revolution, and its Napoleonic aftermath, were, at least, the Beginning of Modern Times.
British historians argue that the Revolution and Napoleon - far from speeding the "modernisation" of France - delayed for many decades the political, economic and industrial developments which were already starting under the ancien régime. The real "beginning of Modern Times" occurred, not at the Bastille or Austerlitz, but in the factories of Lancashire and the West Midlands.
The French see this as a smugly British view of history. By introducing basic property and legal rights - and by the very fact of being a meritocratic upstart, rather than an aristocrat - they say Napoleon hastened the end of feudalism all over Europe and laid the foundations for modern economics and politics.
There is also a suggestion - first made by Napoleon himself over a glass of wine, and possibly arsenic, in exile in Saint Helena - that the emperor was the first "European"; that his intention, all along, was to create a Europe without borders and without "civil wars". To do that he had to defeat Albion by imposing a single European market - "the continental system" - from which the incorrigible and un-European British would be excluded. This theory may be attractive to French romantics, and British Eurosceptics, but it makes little sense.
After Austerlitz, Napoleon was advised by his foreign minister, Talleyrand, to treat the Austrians magnanimously, encouraging a kind of exhausted peace in Europe in which France would be the dominant but not the overwhelming, imperial power. The British, without a serious army, would be powerless to intervene. Instead, Napoleon imposed humiliating conditions on Austria, consolidated his control of Italy and broke up what remained of the Holy Roman Empire.
In doing so he awakened national hatreds which brought about his downfall, nine - and then 10 - years later. He also, accidentally, helped to create the antagonistic, European nation states which dominated the next 150 years and generated two world wars. So much for Napoleon as the "father of the European dream".
None of these conflicting, and confusing, interpretations justify the failure of the French government to mark the battle of Austerlitz properly. As Thierry Lentz of the Fondation Napoleon points out: Austerlitz is not just French history, it is European history. It was not just a military event but a political one.
Commemorated sensibly, and intelligently, as on the whole Trafalgar has been, it could have been an occasion, not for flag-waving, but for contemplating the tangled roots of our common European past. And present.