- France was really big. Much of the diplomatic history of the last century before the revolution had been "France fights everyone and draws". France had by far the biggest population of any European state, and was at the same time the 2nd or 3rd most advanced in its social organisation (more guns, more moneys).
- Revolutionary zeal. In the 18th century, warfare was conducted by proportionately tiny armies led by a collection of heroes, cads, and scoundrels who went around selling their famous services like modern football managers, and soldiered by the sweepings of the street. An actual citizen army determined to defend the country was unprecedented, and the effect it had on recruitment and morale was tremendous.
- Innovative tactics. Simply because they had such vast reserves of poorly-trained manpower to exploit, the French developed the effective use of columns and skirmishers to a much higher level than anyone had in the 18th century. Combined with aggressive leadership, high morale, and the excellent artillery, it took the other armies some time to realise what had hit them.
- Innovative supply system. The French realsied that, when the majority of your troops could be relied upon not to desert, it was perfectly possible to move through the relatively rich lands of western Europe by begging and borrowing. This gave them a tremendous freedom of movement.
- The corps system. Splitting the army up into combined-arms units led by trusted subordinates made it vastly more flexible. Napoleon's ability to send away large parts of his army and know it would achieve wwhat he told it to was crucial in the campaign leading up to Austerlitz.
- Good leadership. Yes, the French favoured promotion by merit; but the other thing to consider is that large parts of the old army had gone over to the revolution (the Emigres were a rather nutty fringe) and brought their considerable expertise with them. The French Royal Army wasn't shoddy. They had even more recently won a war with Britain, known to posterity as the American Revolutionary War.
- Other goodies inherited from the Royal Army. In particular, a splendid artillery. The cannon wasn't a support weapon for the French, but the vital battle-winner.
- The first large army (with no disrespect intended to Suvorov or the Duke of Wellington, but their circumstances were rather differant) to be the battalion-to-battalion equals of the French were the Austrians in 1809. Note that by this time, French tactics have had plenty of time to be adopted and adapted all over Europe; the Austrians have modernised their military system and brought in conscription to make up their numbers; German nationalism is stirring; and in general the Austrians have gained most of the French advantages except numbers. That's what the Wagram campaign came down to: numbers.