Yes, in fact the National Assembly (the revolutionary assembly that was formed by breaking away from the Estates General) had a large proportion of clergymen and nobles. Many of the representatives of the Third Estate (basically everyone from merchants to peasants who weren’t part of the nobility or church) also held titles or were clergymen themselves. Abbé Sièyes is a good example of this, being one of the key revolutionaries in 1789. Part of the reason for this is the philosophy of the Enlightenment, which put forward ideas of democracy and rejected absolute monarchy (in many cases). These ideas were spread mostly within more well-off social circles, with the Palais-Royale in Paris being a centre for the development of revolutionary thinking. Most of the nobility who did defect to the National Assembly came from richer, urban environments whereas poorer, provincial nobles tended to support the monarchy to protect their privilege, which in some cases was the only thing separating them from the unwashed masses.

The Social Interpretation of the French Revolution by Alfred Cobban has a really good insight into the question about how different social groups reacted/were involved in the revolution, so I’d recommend that if you want to look further into this.