You could argue this both ways.
Napoleon was clearly a part of the French Revolution. He participated in the Revolution and was an ardent Jacobin. He is also known for having defended the new government against conservative rebels in the battle in Paris on 13 Vendemairie. So, in this sense, he was clearly a supporter of the Revolution.
However, you can argue that he was not, in the end, a supporter of the values of the Revolution. Napoleon did not, after all, bring about a system of "liberty, equality, and fraternity." He did not create a democratic system once he was in power. Instead, he created another monarchy with himself at its head. In this way, he did not really support the Revolution.
Overall, then, it depends on what it means (to you) for someone to be "for" or "against" the Revolution.