The most relevant change brought about by the French Revolution in relation to Napoleon was the modernization of society, a move away from a feudal society to one where it became possible for people of relatively humble backgrounds to go far in life.
Napoleon was one such person. A Corsican provincial from a family of minor nobles, he rose quickly up the ranks of the French army, taking full advantage of the greater opportunities now made available to those outside the old aristocracy which had dominated society during the ancien régime.
As the French Revolutionaries had swept away the old system, so Napoleon felt able to do likewise once he overthrew the Directory and gradually turned himself into Emperor. The revolutionaries had shown that it was possible to tear up an entire political system, one that had lasted for centuries, and replace it with an entirely new system from scratch.
Napoleon took this lesson to heart and set about creating a whole new political system in his own image, one indelibly stamped with his personal authority. It is almost certainly the case that he wouldn't have been able to do this had the French Revolution not taken place.
Nor would Napoleon have been able to dominate Europe as he did without the prior example bequeathed to him by the revolutionaries. Although the Revolution was carried out in the name of liberty, equality, and fraternity, it quickly developed an imperialistic character as Revolutionary France invaded neighboring countries. Ostensibly, they did so to liberate the people from monarchical oppression, but it soon became clear that these people had simply exchanged one oppressive government for another, a government controlled by the French.
Napoleon took this process a step further, conquering vast swathes of territory across Europe. Though he also used the language of liberation, he wanted to establish a massive French Empire. Once again, the French Revolution, with its imperialistic tendencies, had helped to show Napoleon the way.