Many people accepted Napoleon as the leader, because he was able to do 3 of the following things:
1) Become Popular with the People: Throughout the reign of Louis XIV and Marie Antoinette, their was wide-spread hunger, as the economy started to slack, and the French money became very weak, resulting in pressure for change. However, the Crown Royal failed to address the issues (Louis very little, Marie almost none). As news showed the Royalty living lavishly while the public was barely surviving, it soon led to the usurp of the throne, and the Reign of Terror. With losses on the home-front (with the Jacobins reigning terror on the people), and the war-front (with France losing to her arch-enemies, including Britain, Spain, etc. During this war, an artillery officer by the name of Napoleon Bonaparte soon rose to power as he was able to successfully drive off the Allied powers from being able to take over France. Wide-spread popularity with the public soon gave him the power he needed to rise above the ranks.
2) Replace the 'Terror' with 'Law and Order': When he was not fighting (which was very rare), Napoleon tried to make France better, starting with the Napoleonic Code, which was the law establish by Napoleon & was approved by the people as being fair and just. It set up a fair system (similar too a normal laws) that was able to protect the citizens of France, and was part of the peace after the "Terror".
3) Wide-spread support through large gains and greater influence to the outside: As seen in the short-span of Napoleon's rule, he was able to create an empire that rivaled that of the Roman Empire, and was a capable leader and brilliant general that was able to outwit most of his enemies (though he did make costly mistakes that costed his army, and in turn, his leadership). For example, he was able to cut loss in the Americas for a large sum of money (which in turn was used to fund France and her military ventures). He was also able to add large pieces of territory to France, making her a true "world-power", and feared throughout the years (up too WWII & even now (though not as much)).
There are many more reasons that Napoleon was accepted by the people.
~
