The French Revolution helped to create the idea of nationalism because it promoted the idea that the people owned the state and that the people had an important stake in the state. The French did not have a monopoly on this idea, but it was manifested more strongly in the French Revolution than it had been in any European country up to that time.
Before the French Revolution, people tended to identify themselves more as subjects of a certain ruler. King Louis XIV (who of course ruled long before the French Revolution) could say that he and the state were the same thing and the idea was accepted by many. People did not generally believe that the state was answerable to them. Therefore, they did not feel a strong loyalty to the state.
With the French Revolution, this changed. The revolution stressed the idea that the people were all citizens of the state. This meant that the state belonged to them and should answer to them. In addition, the French Revolution eventually asked all of its members to fight for it in a mass national army unlike anything seen before. Because of these factors, French people came to identify very strongly with the French state. This idea spread to other countries where people came more and more to identify with their governments.
In this way, the French Revolution helped nationalism become more prevalent by promoting the idea that the people should feel an affinity with the state and a sense that they were part-owners of that state.