Edit: to clarify, it just seems that other revolutions had a definite start for the people of the time, like with the American Revolution and the Declaration of Independence. However, in the French Revolution, the National Assembly basically controlled the state while the King was still nominally in power.
Before the King was executed, was there any talk of a revolution occurring, or did the people consider their actions legal, and not a seizure of power?
In fact, the term 'Revolution' was used prior to the generally-accepted beginning of the Revolution. Throughout 1788 and early 1789, particularly after the publication of Sieyés' What is the Third Estate?, liberal intellectuals were calling for a revolution in the French government. It is important to note that 'Revolution' does not only refer to a violent seizure of power by paramilitary forces; especially in the eighteenth century, the term was used to refer to any great change in anything. The liberals and reformers of France wanted a peaceful revolution that would sweep away the irregularities and faults of the ancien régime and bring France into a new, enlightened, and rational era.
The storming of the Bastille and the declaration of the National Assembly were generally regarded as the start of the Revolution, and the feeling in Paris from 1789 to 1791 was that the Revolution would be completed once the Constitution came into effect. Since the National Assembly was, by its own logic, the only legal legislator in France, and the storming of the Bastille had theoretically been in their support (it hadn't, but that was a convenient fiction for everyone involved), there was no question of legality - the Nation of France was represented by the Assembly, and therefore already was the highest power in the land other than the King - and counter-revolutionary moves by the King could be explained away by the idea that they had been ordered by corrupt or reactionary advisers.
Source:
The Oxford History of the French Revolution, William Doyle