The Nine Years War was one of the better opportunities I definitely agree
This book (very readable too) gives the Franco-Spanish a reasonable chance twice before they gave up and committed their resources elsewhere in the American Revolution
https://www.amazon.com/Struggle-Sea-Power-American-Revolution/dp/0393239926
I agree, post French Revolution (and the destruction of the elite corps of gunners as well as the loss of way too many officers) the French Navy had almost no chance at all.
While I agree with you, the French strategy during the ARW was really to support the nascent US by disrupting the British control of the Atlantic and by sending and supplying a well-equipped/well-trained force in America. France never really considered an invasion of Britain, or, to be more specific, wanted to make the British believe that France WANTED to invade Britain, thus forcing the British to divert ressources to protect their coast (the Indian Ocean had the same strategic objective: to force Britain to divert ressources. And it worked quite TBH).
To invade Britain, you need the French to really come up with a different strategy. Plus the War OTL, while it showed the new competence of the French Navy and the capacity to project an army across an Ocean (something France lacked 20 years earlier), really exhausted French finances to the point that the Monarchy was on the verge of collapse in 1783. It means that OTL, France was not able to add another theatre of war (meaning the Channel and Britain). For example, we don't have to forget that Suffren in the Indian Ocean begged for more ships, men and supplies to maintain the fighting capacity of his fleet. France wasn't able to help him and Suffren was forced to recruit Indian sailors to replace his losses, to use captured ships and to plunder British bases to gain wood to repair his vessels. That the man was able to fight and often defeat a much more numerous and better supplied enemy for more than two years shows his great competence as a naval commander. Finally, I will add that the defeats suffered by the French Navy in the Atlantic at the end of the war in 1782 (strategically not decisive but still limitating the potential of the fleet due to serious losses) would be enough to prevent the French to have enough ships to control the Channel (and the British Western Squadron was still here).
So, to have the French trying to invade Britain and possibly enjoying a success, I would see the following options (again, just my opinion here, perhaps it's wrong and there are surely more possibilities):
-One: have a really good commander in the Atlantic. D'Estaing was quite bad and Grasse, while competent, was not great either (his defeats in 1782 show it even it wasn't entirely his fault). Suffren could possibly do wonders. The French Navy in the Atlantic during the war received the best and most modern ships. With those, Suffren would wage a savage guerilla warfare, attacking convoys and limitating (if not significantly destroying) the capacity of the British to send troops and supplies in America. Plus with his tactical competence and natural boldness, the man would be able to defeat the British squadrons during naval battles. This would force the British to send more ships in the Atlantic, thus leaving the British coast less well-protected.
-Second: give up the Indian Ocean theater and keep the ships at Brest. The French Navy, at best, is able to control two theaters, not three.
Result: with a British Navy suffering more losses and forced to send the bulk of its fleet in the Atlantic, the "Royale" could try a raid and possibly destroying or mutilating the weakened Western Squadron. By the time the RN sends ships, the French can cross the Channel and reach Britain or Ireland. Considering the French Army was slightly superior to its British counterpart (250 000 men to 80 000 with both armies having the same quality) in the 1780's, Britain would sue for peace within 6 weeks.
And the Treaty of Paris would be far less benevolent towards Britain with France being in position to force her to give up far more colonial territories (but probably not in India, France was never really interested in India, sugar islands are more likely).