Here's the thing. The Revolution wasn't working great for France. The beheading of the King was only the beginning of the reign of Terror from Robespierre. Revolutionary France was an incredibly violent place, and no solid government was able to maintain power. The Directory was not a good government, full of corruption and orchestrating more killings. Napoleon was not a violent dictator who killed a beloved group of leaders and gained power.

I've argued before that Napoleon is a product of the French Revolution. A Corsican of middle status, the Revolution allowed him the opportunity to rise up through the ranks of the French army and gain more power that would not have been possible in pre-Revolutionary France. Once he gained power, he restructured the entire country, combining ideals from both the Revolution and the monarchy in order to create a powerful, more unified France.

While he may not have been a fairly elected leader, Napoleon gave France what it needed: Strong social relationships, a powerful army and a more unified country.

I can look over past essays I've written about this and provide more detail if necessary.

Edit: Tenses are hard

The series of governments put in place by the French revolution ranged from ineffective to brutally repressive. Between 1793 and 1794 ALONE over 16,000 people were killed be guillotine and up to 25,000 more people were summarily executed. People like Robespierre and others exercised authoritarian power and suppressed dissent while being wildly ineffective and brutal.

By the time Napoleon came on the scene the idealism and hope of the early revolution was dead and people just wanted a competent leader. While many contemporary intellectuals across the world demonized Napoleon for "betraying" the revolution, his rule was by most accounts just and extremely progressive for the time and was certainly an improvement over the monarchy, terror and directorate.

Napoleon's foreign adventures, though eventually disastrous, were initially successful and heroic, an impression that lasted in some quarters even after he was defeated.

The People's Revolution, the first few years of the French Revolution, were surprisingly moderate. People still loved and wanted the king. He once tried to flee to Hapsburgs lands but before he crossed the border peasants recognized him and gathered an army of thousands to march him back to Paris in hopes of thwarting the radicals opposed to him. As the Revolution progressed, the Jacobins eventually turned the people (sanscullottes) against the Girondins and royalist factions in the Revolution and guillotined the king. Robespierre and his Reign of Terror followed. Those radicals wanted to change everything down to the structure of metric time. The French people were still fond of their traditional virtues, but did not wish for a return to feudalism. For a while they knew the only answer available would be the royalists and nobles and they were not fond of that. When Napoleon put down Sardinia and then returned home to deal with the insurrections, the French people saw what they considered to be the perfect compromise, an honorable gentleman with noble values, but committed to spreading liberalism and facing the real tyrants in Europe. It was the reassertion of popular will in a centrist revolution that had become bourgeois or leftist

Because, he was instrumental in saving France from foreign occupation and ensuring the survival of the republic. Immediately following the french revolution the other European powers, (mainly Prussia, England, and the Austro-Hungarians) invaded France trying to reestablish the monarchy. After all, they didn't want the french to set a bad example for their own people. In fact, France was basically at war with England from 1793 until the battle of Waterloo in 1815.

These wars were a make or break situation for the French Republic and required total mobilization of the french population. In fact, this was maybe the first time in history that mass conscription was used. As a result these wars became insanely massive for the time and are generally regarded to be the first modern instance of "Total War", or the complete mobilization of all resources for the war effort.

This kind of mobilization occurred on a scale not yet seen in human history (with the possible exception of Genghis Khan) and required dictatorial powers to accomplish. Napoleon provided those powers and set the precedent for future wars and dictators.

Because he posed himself as an enlightened despot. A believer in liberty and the values of the revolution while standing contrary to the disorder of the Republic and being a strong military leader who had the capacity to help spread the age of reason across Europe. Lets not forget, tyrant he was, but he did many great things and it was Napoleon who extinguished the fires of the Inquisition in Spain etc.. Ending religious persecution, installing secularism and democracy in many local institutions.. And I repeat, he was better than the sort of chaos which prevailed under Robespierre's Terror.

I wouldn't say he is that revered, a lot of people consider him as someone who hijacked the revolution and threw France in wars they couldn't win just for the sake of his own irrealistic ambitions. Comparing someone to Napoleon in France generally isn't a compliment.