It should remembered that, throughout so much of the First Republic, the revolution was in a state of genuine crisis. It faced multiple instances of civil war, including the revolts of the provincial cities against the growing power and influence of Paris (a conflict which pitted the more moderate wing of the Revolutionaries against the radicals), as well as genuinely counter-revolutionary insurgencies such as the war in the Vendée, even as (all the while), France faced foreign war and invasion. As you can perhaps well imagine, such a context would have led to a great deal of suspicion and turmoil.
With the fall of Robespierre and the Committee of Public Safety, the moderates regained power. Even so, much of this political chaos and disorder remained, as the Jacobins (previously empowered) faced reprisals from their political enemies who were now on the rise. Even though the Reign of Terror was over, this sense of internal crisis and internal turmoil would carry through into the rise of the Consulate.
For all of his autocratic impulses, Napoleon was a stabilizing influence within France itself. He restored ties with Rome, which promised to eliminate one of the major rallying cries of the counter-revolution, while mitigating the religiously motivated tensions that had divided the revolution to begin with, and he utilized suppressive tactics to bring provincial rebels to heel. Even as he assumed the title of emperor, he ruled according to popular mandate, holding plebiscites to maintain the appearance of popular support. As is the case with many autocrats and dictators, these plebiscites were heavily manufactured, but even so, it should be noted, Napoleon enjoyed a high degree of popularity within France. And, of course, you should not forget Napoleon's record as a military commander and the expansion of the empire throughout Europe—nor should you forget the Empire's later weakening and collapse.
As for whether it was easy, I don't think it was easy (few things in history ever are), and as to how it would have been viewed in the time, that depends on the political background and loyalties of the person viewing it. A zealous republican probably would have been disturbed by Napoleon's autocratic tendencies, and the reversal of many of the revolution's more radical gains. The majority of moderates, after the turmoil unleashed by the revolution, would have likely been thankful for the reestablishment of stability. Many royalists, on the other hand, might have seen Napoleon as a pretender, and still longed for a genuine restoration. There would have been a wide range of reactions and viewpoints, as there inevitably are in any historical time period.