But again you discussing iotl events. No guarantee of Napoleon rising to power. Almost guarantee not to. When the French Revolution happens almost certain not happen like iotl. French navy could continue to grow and its officers stay unlike iotl.
rherefore everything is up in air.
You may be right. I can't say for sure what would happen without the ARW adding additional debt onto the back of the French Regime. What we can say is the finances of the regime were seriously unsound, and almost irreformable. The social order was also hopelessly reactionary, the economy grossly in efferent. The monarchy was headed by a weak king, who was well intended, but lacked the forceful personality to push through a major reform program.
The king had basically two choices in 1789, to reform the regime. He could stage a coup from above, and brake the power of the Aristocracy, and Clergy, going well beyond what Louis XIV did. Second he could call the Estates General in an effort to forge a compromise agreement. He took the second course. The Aristocrats, and High Clergy had no interest in paying taxes, or giving up any ancient privileges. We know what happened then. The king completely lost control of the situation, and the Ancient Regime fell in blood.
The Enlightenment ideas were already there, they didn't really need the example of 1776, and Tomas Paine's Common Sense. So you could still say even without the ARW that France was a timebomb, waiting to go off. There were just so many resentments just below the surface. It's hard to imagine the Regime surviving very long into even a semi industrialized age. How long can they keep the rising merchant class, hungry urban poor, and landless country people down? The Regime's odds get shorter every year.
Now another question would be just how radical the revolution has to be. A less radical revolution would have made France stronger, not weaker. A reformed France would have had a better chance against the British in a conflict. All war machines rest on the strength of their economies. Napoleon was able to reform the economy, and streamline it, removing medieval impediments. Creating a uniform legal code, and an efferent tax system were huge leaps forward. Land reform helped stabilize the social order in the countryside, and the agricultural economy improved. He tried hard to convince the aristocratic exiles to return, just those naval experts the navy lost in the revolution, with mixed results.
Saying all that the British still have big advantages. Their economy became stronger with each war with the French, and the British Government was always able to finance them. Britain was primarily a maritime power, with strong commercial interests, while France was primarily a land power, with an agricultural economy. French designs were fine sailing ships, yet their British counterparts usually out sailed them. The French Ships of the Line actually carried heavier main armament, but were almost always effectively out gunned. In boarding actions they were usually out fought. In Frigates the British usually out gunned the French, and won about 90% of the time. British seaman were better trained, could fire guns often twice as fast, had higher moral, and their Admirals, and Captains fought with much greater aggression, and confidence.
The same was largely true during the what is called the Quasi War between the United States, and France, to American advantage. The finest hour for the French was the Battle between the USS Constellation and the La Vengeance. The French had a heavier broadside, and a bigger crew, but still lost the battle. In a hard fought action, Constellation fired 1,129 rounds vs. La Vengeance 742. Constellation suffered 40 casualties, vs.160 on La Vengeance. La Vengeance struck her colors twice, but managed to escape when Constellation's main mast fell before she could come along side. La Vengeance had to run aground to avoid sinking.
The French just seemed to be consistently behind the curve. They did well in the ARW, but they still ended up losing the war at sea. In that war they had the advantage of having no enemy on land, so they could concentrate on the navy. It's debatable if they could duplicate, let alone surpass that level of proficiency again during the age of sail. It is possible under the right circumstances, but I wouldn't bet on it.
If you know a lot about naval warfare in this era, lets take a wild hypothetical. After the Battle of Navarino, in 1827 the British, have a falling out with their allies. The French, and British square off in the Mediterranean. France has had 12 years to rebuild their navy, can they match the British ship, for ship, fleet for fleet, sailor for sailor, captain for captain, admiral for admiral. Lay out your own scenario, I'd be interested in what you might come up with.