The meeting took place on May 5, 1789. The Estates General granted the third estate double the amount of delegates to represent their stance due to the fact that they made up an overwhelming majority of the population. This, of course, didn't matter, as votes were cast as entire estates rather than by individual representatives. They refused any further discussion of the issue with the higher classes, knowing their voices wouldn't be heard under the circumstances.
They, then, held a separate meeting with others of their own estate. The group discussed their plans and ideas before designating themselves the title of the National Assembly. Their assembly is intended to allow for proper representation of the people in government decisions. The other estates have been notified of this development and have even offered the chance to join the common-people in their efforts.
The upper estates will, likely, remain unresponsive to their invitations (as the intentions regarding their previous plan of action held seemingly no means of benefit for those whose privilege could be revoked).
As the National Assembly develops a more clear vision for what they'd like for their nation's future, talk of Constitution is sure to become a central topic at future meetings.
If the third estate becomes persistent in pursuing what they want, it could lead to drastic changes regarding the separation of classes (all of which are not likely to occur without a bit of struggle on both sides of the issue). No matter what, whatever happens next is sure to be interesting!
Sources: Louise Élisabeth Vigée Le Brun [Public domain], via Wikimedia Commons.; Joseph Duplessis [Public domain], via Wikimedia Commons.; History Staff. "French Revolution." History. A&E Television Networks, 2009.; Thor. "National Assembly 1789 (France)." History Wars Weapons. N.p., 11 Apr. 2011. Web. 18 Jan. 2017.