It is, of course, impossible to know for sure why people do anything. However, we can speculate that the French embraced Napoleon for two reasons.
First, we can say that they did so because he portrayed himself as (and in some ways really was) a son of the Revolution. Napoleon did not come in to overthrow the gains of the Revolution but to consolidate them. For example, while he did make himself all-powerful, he did not return power to the aristocracy or to the Church. In a sense, everyone was equal under him. This made him more acceptable to the people.
Second, the Revolution was a very chaotic time. In times of chaos, people seem to seek strong leadership. They want someone who can bring their lives back in to a more orderly and secure state. Therefore, they would have been more willing to support someone like Napoleon who seemed to be able to end the chaos of the Revolution and restore order.