I don't know either period well enough to sharpen this question. It just occurred to me to wonder what the answer was as I thought about how important French troops were at the Battle of York and how Napoleon's efforts to challenge the British navy only a couple of decades later failed utterly - or so I have heard.
Edit: Took out an unnecessary word.
To answer in short, it was because the French Revolution's various purges stripped the French Navy's leadership of it's (mostly) Royalist-leaning, noble-born officers and administrators. Throw in the fact that the French fleet got beat up pretty badly during the Seven Years' War; the British even called 1759 the year of Annus Mirabilis, due to the fact that they won some pretty astounding victories on the water over the French, most notably the battles of Quiberon Bay and Lagos, which were massive tactical and strategic losses for the French, along with the hulls and sailors they lost.
The French spent the next 20-ish years trying to rebuild, and managed to a certain degree Maybe not quite on par with Britain's Royal Navy, but certainly a threat to be reckoned with. When the Revolution kicked off in 1789, a lot of officers that supported the Royalist cause (or were just nobles themselves) were either swept up the various purges, or ran off to foreign lands (a lot wound up in America), or were stripped of their commissions and kicked out of the Navy.
To add insult to injury, the National Convention (one of Revolutionary France's constantly-changing governing bodies) dissolved France's Fleet Gunners School, which (obviously) instructed a lot of officers and gunners on the art of gunnery afloat. This resulted in a massive shortage of skilled gunners; as the ones who had training aged out of the Navy or were pulled off ships to go manage coastal fortifications and siege trains after Napoleon took power, there were just fewer experienced gunners to go around. Inefficient gunnery loses battles, when you're talking Age of Sail tactics; which, mostly, consisted of lining fleets up against one another and dumping cannon fire into the enemy until somebody gave up.
Also, that depleted officer's corps was mostly reconstituted using junior officers with Revolutionary sympathies, and promoted warrant officers. There are many instances of French ships being captained during the Napoleonic Wars by guys that were, in effect, just jumped up Bosun's mates. Fine sailors, maybe, but lacking the finer points of skills like navigation and how to lead a whole ship's worth of sailors. Napoleon's chosen leader for the French navy (Vice-Admiral Louis-René Levassor de Latouche Tréville) was a very skilled sailor and administrator, and spent the years 1800-1804 doing his damndest to refurbish the French naval system, get better training in place, etc. Unfortunately for Napoleon, he died of an illness in 1804.
Also, the British Channel Fleet was really good about blockading most of the major French ports. A ship stuck in harbor is effectively useless.
The Battle of Trafalgar (1805) was pretty much the death knell for the French Navy; they and the Spanish lost something like 14 capital ships between them. That's a lot of first, second, and third-rate hulls to replace, along with the sailors attached to them.
Sources:
The Age of the Ship of the Line: The British and French Navies, 1650-1815 (Studies in War, Society, and the Military), by J. Dull
In Nelson's Wake: The Navy and the Napoleonic Wars , by J. Davey