Could the French Monarchy have been saved or was it doomed to fall from the start of the Revolution in 1789?
I would have to agree that the way the class system and taxation system was set up a revolution was indeed inevitable. The lock out of the Third Estate from the Estates General led to the Tennis Court Oath and provided a rallying point for the revolution.
The French Monarchy could only have been saved if a strong monarch had ascended the throne who could force the Nobility to assume some responsibility for paying taxes. Under the existing structure (the "Ancien Regime,") only the peasantry paid taxes; this group, the third estate, included the wealthy Bourgeoisie. The tax base had been narrowed significantly by creating new titles of nobility, so called "Nobility of the Robe," who for a fee, paid no taxes. The title was inheritable, so their heirs in perpetuity paid no taxes either. This, combined with the enormous debt France had encountered by reason of a number of European wars and participation in the French Revolution, put the country in a downward spiral. Louis XVI was weak and somewhat disengaged from the populace, and was married to an Austrian to boot. He did not have the stomach to stand down the nobility; and called the Estates General instead. Absent an unusually strong leader, the revolution was inevitable.
There is, of course, no way to know this for sure. We cannot go back and play the Revolution over and over again changing things and trying to see if the monarchy will fall every time. I would argue that the monarchy could have been saved, but that it would have had to change much more than the actual ruling class were willing to do.
If the rulers of France had been more flexible, they might have been able to save themselves. If, for example, the First Estate would have been willing to allow a fairer tax structure to be imposed, the Third Estate might not have gotten as angry as it did. The ruling classes of France would have had to make very serious concessions, but if they had, there is no reason (to me) that they could not have continued to head the country in a constitutional monarchy. After all, it worked for England, so why could it not have worked for France?