I think that the French navy is being sold too short, concerning at least their long term capabilities to build up a force to defeat the United Kingdom. Generally their early opportunities are pretty limited; maybe they could have had a shot around the Trafalgar period if they had better concentrated their fleets, at least enough to keep them in a better position for later, but they're facing a superior number of enemy ships from a position of qualitative inferiority at that time. However, I am of the opinion that if the Peninsula and Russian campaigns are won, then the French fleet will be able to in time outbuild the Royal Navy to the extent than quantitative superiority will be able to defeat whatever elements of qualitative inferiority it has, and that its qualitative inferiority will be reduced.
Under the Ancien Régime, the French were able to finance and support a fleet of 80 ships of the line during the decade. This was generally near the maximum of their capabilities, and there were at times difficulties reaching the number, but this did represent what they aimed for. The British by 1810 had 152, which was probably near the maximum amount that could be supported. Given that France under the Ancien Régime could support 80 SOTLs, given their serious financial system problems and taxation issues, then Napoleonic France, which had achieved significant advances in regards to the financial system - with a stability of bonds that outmatched their predecessors, the end of the parasitical noble class' tax exemptions, significant direct territorial expansion, and an unprecedented expansion of French power in Europe, should be able to support far more. I vaguely remembered that there was a 150 ship of the line plan, but I'm unsure if this is just my memory confusing it with the number of ships the British had, or otherwise just pulling the number out of the air. Regardless, the French Navy was undergoing an expansion during the last few years, and if that was correct, then they'll be able to achieve numerical parity with the United Kingdom for the first time in a long time. The British, given financial difficulties - the Continental Blockade will become tighter and the remaining nations that aren't part of it are removed, and will be less often willingly skirted by the French themselves, as French power is solidified - as well as the number of sailors they have, which must be limited, will have severe difficulty further expanding their fleet. Of course, they can make up trade with non-European countries, but that can only go so far.
Not everything is rosy for the French Navy of course, in that unless if the campaign in Spain went much better and decisively won quickly, then the Spanish contribution to the French navy will be much reduced. According to Wikipedia at the time of Trafalgar they had around 45 ships of the line, a reasonable force. This had disintegrated to 28 by 1810 and 16 by 1815. If Napoleonic France is able to win the Peninsula campaign, then the Spanish government might be able to be brought onboard, which even if they are badly deteriorated should add a few dozen ships of the line to the French fleet. I'm reading fleet strengths for this off of
a post on History Stack Exchange btw and I'm not sure if the 1810 numbers for the Dutch reflect being annexed in that year by France or not, but I'll assume that is their pre-annexation numbers. So that too, should add on additional ships of the line, and the French were building ships of the line in Dutch shipyards post-annexation. While I presume that the Russian fleet wouldn't be utilized on the French side, it also presumably would be denied to the British side, and while Denmark's fleet had been destroyed by the British attacking it when they tried to defend freedom of the seas or because the Danes refused to simply give it up to them, they were playing an important role with lighter ships such as gunboats.
In addition to the problems of finance, a major problem faced by the Ancien Régime was acquiring sufficient timber and naval supplies. These came from the Baltic for the French Navy. While the question of transport remains, there should be much better control over the sources of supply, as well as their denial to the British (the British can go elsewhere such as to North America and India - which seemed to have a surprisingly good shipbuilding capacity and in addition good forests - but its still worth something). So, building the ships shouldn't be possible, in addition to all of the shipyards that the French have throughout their possessions. This was generally a success of the Royalists, who had done impressive infrastructure work on Toulon, Brest, and Marseille, as well as started on Cherbourg - a project continued by Napoleon.
The French officers corp was generally well trained (the French Navy pioneered its officer training during its 17th century build up), and the horrible social battles of the late Ancien Régime navy were, so far as I know, settled by the Revolution. The Royalist navy was suffering from a conflict between common officers and professional ones, and also between sea-going officers and administrative officers. As with any bureaucracy, the iron law had come into effect by the end, where the bureaucracy exists to serve the bureaucracy. Instead of the small and efficient administration established by Richelieu and Colbert, the French Navy's administration was being buried under clouds of parasitic noblemen who never went to sea, and who never even had to leave Paris. Sea-going officers (Officers of the sword) felt they were under the control of idiots on land who didn't know what they were doing, while land-based officers (Officers of the pen) felt that the sea going officers were unprofessionals. After the Seven Year's War there was an attempt to promote promotion from personal merit (actually long established in the French navy), but this was badly conducted and often elevated people without regard for the officer corp's chain of command. This led to acts of insubordination and a growth in discontent among the navy's officers. Meanwhile, the influx of commoners from the merchant marine led to its own conflicts in the officer corps.
I haven't read much about the social history of the Republican and Napoleonic navies, but while it is obviously clear that the Republican period saw a general deterioration of the Navy's standards, it also would have logically solved the conundrums by eliminating the nobles, pressing affairs solidly in favor of the commoners, and wiping the fleet out and enabling things to get started from a clean slate. Its hard to have a long-running dispute between commoners and nobles when all the nobles are dead and the noble pen-pushers have had their heads chopped off. Thus, the French Napoleonic Navy may be starting from a lower level, but it has much greater potential than the Royalist fleet, the same story as in the French Army.
Sailors is definitely the weak point for any French fleet, this can't be ignored. The loss of so many ships, the confinement of the remainder to harbor, the blockade on French shipping, all will do a lot to prevent the French Navy from being able to reach the same standards of seamanship as the British. Still, they can do a lot to improve. For example, one of the primary problems with French gunnery vis a vis British gunnery, as far as I understand, was slower rate of fire. A continual problem faced by the French was insufficient powder reserves - although the genius of French chemistry had enabled them to have sufficient domestic saltpeter production to avoid having to import from India or run out, although that has its negative aspects for fertilizer production - which I presume had far more to do with the French not drilling their troops more for firing than any inherent superior British training desire. If the wars on land have ended, presumably it won't be hard to allocate enough powder to the navy to be able to improve gunnery standards, something that can be accomplished without spending too much time at sea. They'll also have access to Dutch sailors after the annexation of the Netherlands. If the French can reach a number of ships close to the Royal Navy's fleet size, then given the problems of maintaing a blockade (is it either 3 ships or 5 ships needed to maintain a fleet on station? I think its 3, you have 1 at home overhauling, 1 in transit or something similar, and 1 on station, but I'm not sure; regardless only a fraction of the fleet can be continually at sea), they'll start to be able to put their fleet to sea much more aggressively, which will give them chances to train their fleet. They won't be able to soon match the Royal Navy seamanship wise, but as the quantitive gap will start to narrow.
In general I think the entire debate over how good each side's ships were isn't very important, and resembles the pointless discussions about making modifications to some obscure airplane or tank on Post-1900. Sure, equipment superiority gives its advantages, and whether one's ships are faster and better sailors has its important points, but its always the morale, training, experience, logistics, doctrine, and command that plays the vital role, not equipment. There exists enough arguments over which side is better that the difference can't have been too large after all; if it was a one sided issue and the French navy was clearly inferior, then we wouldn't be arguing it. Furthermore, for the scenarios that I've outlined concerning brief expeditions outside French ports with massive naval superiority to train, given that the French can choose what weather to operate in, the quoted lighter build of their ships and better blue-skies seakeeping superiority would come to the fore compared to presumed more rugged build of British ships - if this is true, concerning stated British naval construction superiority regarding such strengths.
Finally, while losses were clearly in the favor of the British throughout the entire endeavor, as on land the defeated party tends to suffer disproportionally heavy casualties due to resistance breaking down and getting captured, no? This is further compounded since ships sunk during the period are limited in number and most casualties come as a result of one side capturing the other; since the British generally won the naval engagements, their enemies thus "lost" more ships than the actual combat conditions would necessarily pertain to.
So no, I don't think that the French building up in time a navy capable of matching and defeating the Royal Navy, given a continental victory, is impossible. Of course, the question may be asked why they haven't come to terms by then; if the French have achieved total and complete domination of the content, and the British don't have any allies there, and the French navy is carrying out its naval construction program, well peace would presumably have come long before the French navy had to actually be put to use.
This leaves the Napoleonic navy unable to win a war against the RN. Battles - with a massive superiority in numbers (Trafalgar was c.2:1 and a drubbing for the allied fleet, so likely to need 4:1) it would be possible to win a battle, but I would expect indecisively - the superior seamanship of the RN would enable them to disengage.
*Check's wikipedia*
Franco-Spanish fleet: 41 ships, with 18 French ships of the line and 15 Spanish
British fleet: 33 ships with 27 ships of the line
When did 33 Franco-Spanish ships of the line vs. 27 British ships of the line become "2:1" in the Franco-Spanish favor? That is 1.222… times larger than the British Fleet, not 2 times the size.