The First Estate, as with all monolithic groups, was not united in it's reaction.

There were some who thought it would eventually blow over. The thought was that the King would have a semblance of power over the Revolution (until he lost all the power) and that people would respect his position as King (which in the end, they didn't). The problem is that most people didn't know how the series of events were going to fold out, and they were more interested in returning to their way of life.

Then there was those who actively supported the Revolution. Here you have people like the Philippe Egalite, Duc de Orleans and cousin of the King or the Marquis de Lafayette. Both supported the Revolution and the reform it would bring but the Duc de Orleans had an alternative interest, hoping he would become King after they deposed the unable Louis XVI. Eventually the duke would meet the same end as the person he hoped he would replace.

Lafayette however ended up fleeing France when he realized the change in politics. This would represent another set of those in the First Estate, the emigre population. Much of the nobility simply packed up and left France for their own safety. Unlike what the Jacobin propaganda might say, the nobility cared about their family and didn't want to see them getting their head chopped off and put on a pike (as it happened to the Princess Lamballe). Many ended up serving in foreign militaries for the express purpose of putting down the Revolution.

However, there is one final group, those who participated in the Revolution but were quiet and did their duty. Here, you have members of the petite noblesse that were unimportant to the higher nobility but also interested in serving France. The son of the duc de Orleans (while not petite noblesse) served in the Dragoons and fought at Valmy. Others like Louis-Nicholas Davout served in the army with valor and bravery. Of course there is only one petite noblesse that rose even higher the rest.