Great post, John!
Well, I think France had two 'peaks' when their naval designs - especially their frigates - were superior to that of other nations; first one was the tenure of Blaise Pangalo as master shipwright at Brest at the turn of the 17th century, second one was when Blaise Ollivier held the same post for a rather brief period in the middle of the 18th century. After all, it was him who finalised the design of the 'true' sailing frigate - i.e. a cruiser with two continuous decks - and the famous 'apple-shaped' body that was so typical of french (and danish) frigates until the end of the Napoleonic Wars.
It´s a pity Ollivier died before he could contribute to the next step in frigate design, building larger ships that could carry a battery of 12-pounders. So it was up to Sir Thomas Slade to develop the 'stars' of this class, the Nigers and the Lowestoft. These ships set the standard for this type of frigate in the middle of the 1750s and still were at the end of the 18th century ( honourable mention goes to the american Hancock and Guignance´s Dédaigneuse-class, though).
Which 18-pounder class was the 'best' is up for debate. Maybe Rule´s Livelys, maybe Sané´s Pallas-class, maybe even Constellation/Congress.
When it comes to 24-pounder frigates and when we take into account what BW posted above - cruising endurance, cost, manning requirement, firepower, speed, stability, strength, longevity - , then there´s only one pick for me, af Chapman´s Bellona-class.
La Forte/L'Ègyptienne supposedly had their problems with strength/longevity and the United States-class falls a bit short in the cost departement