Not only that but how did the French people feel about him after his coronation? They went from the Directors, to the Consuls to a full blown Emperor leading them before the Coalition wars. There had to have been some problems right?
When Napoleon was chosen to become a Consul by Sieyes, Sieyes thought that he could simply use Napoleon as the strong arm to his more political mind. He didn't anticipate that Napoleon would push Sieyes away and create a Consulate with his supporters. From here, he structured the French government to completely be packed with supporters and set it up so that the legislature was more of an advisory body rather than an independent body.
From here, Napoleon basically ruled without anything to stop him. Although this sounds bad, his years as Consul are generally considered to go very well with one of the few exceptions being the death of the Duc D'Enghien.
The path to the empire was a very gradual process between 1799-1804 which meant that Napoleon possessed a degree of flexibility when it came to his self-coronation. There were two trends at work in France at this time which help explain why this transition was relatively smooth. Firstly, Napoleon greatly benefited from and actively encouraged a depoliticization of the French government. The consulate's emphasis upon the power of executive authority greatly helped in this manner as it became much more difficult for the Tribunate or the Senate to form an alternate power bloc against the First Consul. Napoleonic censorship also denuded the republicans remaining within the French government of any organs which to voice opposition. The Consulate did witness some friction between Napoleon and the other branches of government. For example, Napoleon's partisans within the government had to work quite hard to get the various organs of state to pass much-vaunted Légion d'honneur, which the remaining republicans in government saw as an affront to the history of the Revolution. Napoleon responded to opposition with a measure of tact that mixed with an iron determination to get his way. Napoleon rewarded his loyal servitors with new titles and estates. He also though expected these servitors to exhibit a degree of competence and was a very stern taskmaster for the running of the French state. Napoleon also acted quite differently than other French executives towards opposition. Lazare Carnot, one of the unimpeachable heroes of the Revolution, exemplifies how Napoleon defanged his opponents. Carnot was one of the stalwart foes of Napoleon's accumulation of power. When he voted against the making Napoleon consul for life in the Tribunate, he had it put into the official record that by voting no, he had written his own condemnation. In prior regimes, this would have been a death sentence, but Napoleon allowed him to retire and function as a private individual in the empire. LeBrun, the third consul and the most republican of the trio, similarly was also allowed to play a less active role in French politics, while still receiving titles and rewards. The other consul, Cambacérès, became Napoleon's right-hand man within the imperial state and also was a beneficiary of Napoleon's largesse. In short, the French government became both pliant and reasonably competent by the time of Napoleon's coronation.
The second trend at work in France at this time was the image of Napoleon himself. Napoleon enjoyed an unprecedented degree of popularity during the Consulate. The period of 1800-04 was a time when Napoleon scored a number of diplomatic coups that greatly added to his prestige. Even though it was short-lived and fundamentally unworkable, the peace with Britain was an accomplishment that no prior Revolutionary government had accomplished. The Concordat with the papacy also seemed to be ushering in a period of domestic peace within France. This is why the 1802 plebiscite for a life-consulship received a broad base of support, even if the Napoleonic state had its thumb on the scales. The public image of Napoleon also underwent a profound transformation at this time. Napoleonic artists tended to less depict him as a republican general and much more as a regal figure who employed the gestures and symbolism of monarchy. As with the government, Napoleon rewarded loyalty to the increasingly personalist regime amongst the public while side-lining any opposition. Fetes, public festivals and new forms of imperial nobility had a strong element of a cult of personality about them, but they also were enjoyable distractions.
The question as to how deep this support for Napoleon ran both in the government and the public though is an open one. While Napoleon was a popular figure, the expressions of popular support such as petitions to name him a hereditary emperor were definitely manufactured. For instance, there was a clear connection between the army's leadership drafting these petitions for the ranks to sign. The empire's fetes surrounding the coronation were large, but a number of observers noted they were not particularly boisterous. There was also a great deal of apprehension about the hereditary nature of the empire within governmental debates. The issue of succession was far from clear in case Napoleon died or was otherwise incapacitated. Although Napoleon's nominal heir was the son of his brother Louis and step-daughter Hortense, the succession issue was something quite vexing to the French government. Underlying this anxiety is a fear that the entire imperial edifice rested upon the shoulders of one man, Napoleon. Herein lies the double-edged nature of Napoleon's path to power. He constantly portrayed himself as an extraordinary individual who operated outside the limitations of normal human beings. The justifications used for the transition from a consulship to a hereditary emperor explicitly stressed this. But this type of rationalization ensured that it was much harder for anyone to follow him. So in the end Napoleon, much more than Louis XIV, encapsulated the dictum "I am the state," which ensured that Napoleonic empire was hostage to its emperor's personal fate.
Sources
Bergeron, Louis. France under Napoleon. Princeton, N.J.: Princeton University Press, 1981.
Dwyer, Philip G. Citizen Emperor Napoleon in Power. New Haven, Conn: Yale University Press, 2013.
Woloch, Isser. Napoleon and His Collaborators: The Making of a Dictatorship. New York: W.W. Norton, 2001.