While I can't necessarily speak to Napoleon's popularity outside France, within France he was, broadly, popular - as a general, he had given France victory after victory; as a statesman, he had reached a concordat with the Pope and ended the war in the Vendée, thus removing two of the most potent sources of internal danger for France - but only at first.

General Bonaparte (as he should properly be called prior to he accession to the Imperial throne) was already de facto the autocratic ruler of France in 1802 upon the plebiscite which confirmed the Life Consulate, and had made good on his promise to bring France peace and reconciliation. He had even managed to somewhat stabilise the French economy. Most importantly, he had given France stability. The Revolution, whether we're talking about the liberalising monarchy, the era of the Convention, or the Directory, had been an unstable phenomenon, constantly shifting from crisis to crisis, and almost always at war. The Consulate that Bonaparte had gained control of had finally won the war that had lasted almost constantly since 1792 - or had ended the war in a way that looked like a victory to the French people -; it had finally codified a new code of law, and, most importantly, it had provided stable government. These factors continued to gain him popularity after his accession, and the lavish ceremonies he organised in Paris helped keep the urban population on-side.

During the consulate, Bonaparte had carefully isolated the most ardent Jacobins from power - in many cases, impriosning or exiling them from France. Particularly, general Moreau, who had been one of the other generals who might have become First Consul in the coup of Brumaire, was brought to trial in 1804, but he proved so popular - the court guards saluted when he took the dock - that Bonaparte had to accept a very reduced sentence of exile. Those who remained - broadly, those who either were willing to bow to Bonaparte's wishes or who had significant support in the Army - were integrated into the Consular, later Imperial, government. He also removed people who might otherwise be dangerous - Germaine de Stael, one of the liberal nobles who had been part of the Revolution from the beginning - was finally exiled by Napoleon due to her opposition to his autocratic tendencies.

The renewal of war in 1805 did serious damage to France's economy, but the stunning victory of Austerlitz and the consequent position France enjoyed as the most powerful nation in Europe did a lot to shore up Imperial support.

Napoleon helped maintain support through a massive array of propaganda, titles, and advancements. Those who were willing to bind themselves to his service - particularly young, competent men - could rise incredibly high in the civil government. Military officers who excelled would find themselves made Count of whichever place they helped the Emperor had won a victory (this became a Duchy for members of the Marshalate, and Marshals were often given Princedoms as well). Napoleon exercised almost complete control of the Press, which trumpeted his victories and downplayed his defeats. Indeed, it sometimes made up entire battles to give Napoleon some victories when that was needed. Further, he inherited an extremely efficient secret police from the Revolution and used it to its fullest extent, removing agitators against Imperial rule.

However, this popularity didn't last forever. Napoleon's policy of reinforcing the Grande Armée by yearly conscriptions became incredibly unpopular, especially as French wars grew farther and farther away from France and seemed to be fought for the aggrandisement of the Emperor rather than the defense of La Patrie. This wasn't helped by heavy casualties from 1808 or so on, which after 1812 led to conscription being viewed as a sure path to an early grave. The propaganda machine's incessant glorification of the Emperor completely discredited it, and even when it did start reporting the Emperor's defeats, the general public had taken to ignoring its bulletins. Further, the system of titles and advancements turned against Napoleon, with the grandees of France becoming more protective of their own positions than that of the Emperor, which eventually led to the Marshals forcing Napoleon's first abdication at Fontainebleau in 1814, and the relatively peaceful transfer to Bourbon rule in that year.

Sources/Further reading:

The Napoleonic Empire, Geoffrey Ellis

Napoleon Bonaparte and the Legacy of the French Revolution, Martin Lyons

Taking Liberties: Problems of a new order from the French Revolution to Napoleon, edited by Howard G. Brown and Judith A. Miller

The Oxford History of the French Revolution, William Doyle.