This is a relatively difficult question to answer. For a start, while Napoleon became Emperor in 1804, his actual level of power and control over France didn't really change much; he'd been First Consul since 1799 and had effectively held absolute power since 1802. What the declaration did was change him from a dictator to an absolute monarch; in theory, this would be a serious problem for anyone wanting to rule over Revolutionary France, but the way in which it was achieved gave Napoleon significant legitimacy.

When Napoleon was crowned in 1804, he was not crowned 'Emperor of France'. Instead, he styled himself 'Emperor of the French'. This, while a semantic difference, was significant: Napoleon ruled as the head of the French people, not simply the overlord of an arbitrary parcel of territory. This style was justified by the mechanism of the change from Republic to Empire. Instead of simply declaring himself Emperor, Napoleon held a plebiscite - a national vote on handing the government of the Republic over to an Emperor.

This plebiscite was almost comically corrupt. The official rolls count over 99% of votes in favour, with the Army and Navy granting votes collectively rather than by individual. Over half of the eligible voters did not vote. Even those who did vote in favour expressed concerns: one notes that while Bonaparte clearly deserved a throne, they worried about the suitability of his heirs.

The press was by this point thoroughly restrained by the regime, and it was impossible for them to register a protest. Most of Napoleon's political opponents had been removed from public life in 1802, and the police had wide-ranging powers to capture enemies of Napoleon. With that being said, even if there was widespread discontent, we don't see major rebellions breaking out in favour of the Republic. Unlike on Napoleon's return on 1815, or throughout the Revolution, there are no major insurgencies within France on Napoleon's assumption of an Imperial title, and no major military figures express public discontent. The government of France had, after all, not actually changed; all that had really changed was that Napoleon was now called Emperor, rather than First Consul, and that his son would inherit the throne after him. As he didn't have a son, this was a problem that could be dealt with in the future.

Napoleon was generally popular (as far as we can tell) within France at the time; he could claim to be the military saviour of France due to his actions in 1800 against Austria, although the brunt of the fighting was done by other generals; he had successfully brought a settlement with the Catholic Church and with exiled nobility; he had finally ended, through threats, military action, and bribery, the insurgencies in the Vendée and western France; and he had reformed the tangled mess of Ancien Régime and Revolutionary Law into the Civil Code.

Napoleon's popularity waxed and waned with his military fortunes. His control of the press enabled him to put out propaganda in a way unknown in Europe at the time, and in the early years of the Napoleonic Wars, public opinion broadly held him in good favour. As he was technically fighting a series of defensive wars (against Austria, Britain and Russia, and later against Prussia), success enabled him to portray himself as the defender of France and its enlightened ideals against the jealous crowned heads of Europe. Once success waned, however, as more and more men and boys were called up, and as the Continental System and repeated invasions of theoretically-neutral states made it clear that Napoleon had become an obstacle to peace in Europe and the source of France's constant wars, opinion soured. The press became ignored as hogwash, even after it started admitting defeats, and while Napoleon was able to rally a last gasp of support in 1814 for the defence of la patrie itself, he'd lost the most significant source of support he had: that of his Marshals.

Napoleon's support on his return was far more contested: his route was specifically chosen to avoid areas where he might be arrested or killed. In the army, officers (not usually enlisted soldiers) had to choose between their oaths to the King and their loyalty to the Emperor. Most chose the Emperor, but a significant minority fled the country rather than forswear themselves. The army generally preferred Napoleon in 1815, due to the ways in which the King had treated them; in particular, the order to melt down the Eagles, which many soldiers had fought and bled to defend, carrying them out of Russia or pulling them from muddy German fields so they would not be captured, was massively unpopular. Napoleon also sought to portray himself as more radical and revolutionary in 1815 than he had before, casting himself as the last gasp of Revolution, a brave resister of the Vienna System now under construction. This was partially successful at best; rebellion broke out in the Vendée, the middle classes never particularly rallied to his side, and Napoleon's control unravelled after Waterloo.

Sources:

Geoffrey Ellis, The Napoleonic Empire

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

Clive Emsley, Napoleon