A few points have to be made beforehand here.

First, the French Revolution wasn't really a "commoners" revolution, the ideas behind it were from the "bourgeoisie". At the beginning of the Revolution the commoners were "used" (for lack of a better term), while they were manifesting because of a lack of food. The 14 of July 1789 had 2 revolts, one from the "tiers état" representative, and one far more mundane manifesting for food, the things is that they "merged" and started the Revolution as his. (It is grossly oversimplified here). The removal of the King, destruction of the nobility and “hatred of the aristocracy” was part of the Terror. Without going to much in-depth (partly because I don’t know enough about the Terror), this period was … troubled. Many political ideologies emerged and fought for control over France, ranging from Royalist, to the Jacobins which were the most radical fringe of the Revolution. At that point we have France which is in a state of quasi civil war, and most of the European Monarchies are looking at the Revolution with fear. And they attacked France on multiple fronts. To just sum-up the French situation before Napoleon rise: A country on the brink of Civil war, attacked by most of Europe.

Napoleon rose so quickly in France for multiple reasons, first and most importantly, his military success in France and Italy, where he crushed Austria and participated in the treaty with Austria, this made France the major player in northern Italy. His campaign in Egypt, while unsuccessful still brought him some “prestige”, notably by bringing back the “Luxor Obelisk” and the “Rosetta Stone”. His campaign in Egypt, turn short notably because of the difficulty to break a siege in Syria (where he was fighting England), but also because he and Emmanuel Sieyès (a political ally), feared a counter-revolution, and once again France was attacked by some of the Europeans power.

Sieyès fearing the counter-revolution and in front of the risk of invasion wanted a military dictatorship and asked Napoleon to come back. When Napoleon finally arrived in October 1799 the need a military coup was not present anymore. France had won decisive victory in Switzerland and Holland, moreover the counter-revolutionary failed their attempt at grabbing power. But still the 8 and 9 November 1799 Napoleon and Siyès did their coup, and created the “Consulat” which was led by three men, Siyès, Pierre-Roger Ducos and Napoléon. Even if this “triumvirate” formally existed, it was Napoleon that was ruling the country.

I won’t go into details about how the 5 years in-between the Consulat and his rise as the Emperor (partly because it would be way too long), but I’ll try to put the short version.

He reformed the administration, modernizing it and rationalizing it. He helped developed the educational system, reformed the economy, created the base of the civil law (which was the base to many modern corpus of law), reconciled the Church and France, developed the army and the formation for officer, promoting the idea of a meritocracy (especially in the army)….

France was still at war with many European power, Napoleon defeated them (Austria in particular) and expanded the frontier of France during the process (in 1801). Great Britain signed the Treaty of Amiens (a peace treaty) in 1802. Year were a popular referendum elected him as “Consul for life”.

Finally, he was able to claim the title of Emperor “thanks” to the context, Great Britain plotted to assassinate Napoleon and they financially helped Royalist in France, both failed. The idea of claiming the title of emperor supposedly comes from Fouché as a way to discourage conspiracy. The idea being if the title is transferred hereditary it won’t matter if he dies the political structure should survive. But I assume that Napoleon was also eager to be crown Emperor if not just for the title, the man was ambitious and tried to emulate many emperors during his carrier (Alexander, Caesar, Charlemagne…). Anyway the empire was proclaimed the 28 may 1804.

They weren’t many revolts because of the prestige of Napoleon, after all the man was changing France in many way that were seen as good (defending at least part of the idea of the Revolution), he was the leader that defeated time and again the countries that attacked France, and he assured the French position in Europe by taking some very rich land (Holland and most of norther Italy) and keeping under control Switzerland, and some German Princes.

He was also liked by the Church and the army for the most part revered him at that point. They didn’t “handled him the key” but by that point he could have claimed practically anything and had France follow him. In 1804 no one contested his claim because he was Napoleon, the man who was seen as a hero and the greatest defender of the Revolution. Moreover, here I’ll speculate a bit so take it with a grain of salt, I imagine that after what is essentially a little more than 10 years of war/civil war/coup/counter-coup, the French of the time were quite happy to have a somewhat stable government. The Empire didn’t change the political structure of the Consulat that much so it was “just” a simple evolution in the term used to describe the Leader of France.

Hope this helped. And I’m sorry if I made any mistake in English, it’s not my first language. Same thing if I made any mistake on the history part I really want to know what. Main source (mostly to check the dates and note write anything stupid): https://www.britannica.com/biography/Napoleon-I#ref16219

You have given an excellent response to my query. Thank you very much.