1. The Acheron of the movie never existed, but description of it in the movie's dialogue conforms to the American Constitution class 44 gun frigate.
2. In the original book of the same name, Jack Aubrey and HMS Surprise pursued a ficticious 38 gun American Frigate USS Norfolk halfway around the world until the American ship wrecked in a SouthSea storm.
3. Historically the British Frigate HMS Phoebe did in fact chase the American 32 gun Frigate USS Essex halfway around the world and then destroy her in a long range gunnery action. It seems likely that the book, and more indirectly the movie, was based on this incident.
4. Clearly a movie showing the British successfully defeating an American Frigate would not sell well in the United States, so it made sense to change the enemy to the French, whom most Americans could be made to hate with the slightest provocation at any convenient time.
5. It also makes sense to stack the odds even more dramatically against good guys so as to heighten the drama, thus the opponent not only changed nationality, but was also uprated from a 38 gun, 18pounder frigate to a 44 gun 24 pounder frigate.
6. But the stretch is not so far fetched. Although Americans idolize the Constitution as the super Frigate unmatchable by another other frigates of the world, in fact that French had been building Frigates superior to the Constitution since the war of 1756, and had a number of 40-50 gun 24 pounder frigates in commission during the Napoleonic war.