Excellent questions.
****Is it possible that the French horn players, played the piece exactly as they intended. ****
Unlikely. Choice of volume, blend and tone, possibly. Those are aesthetic choices in part dictated by the conductor. However, out of tune playing is never a desirable choice. The French players were very out of tune; better in tune playing can sometimes be perceived as "smoother". The English Baroque players are simply better players. Having said that, it is probably true that orchestras back then did not demonstrate the often flawless intonation heard from modern orchestras. This is due not only to today's, overall, much higher technical standard on the part of players, but also the superiority of modern instruments. I suppose an argument could be made that "rough-around-the-edges" playing was, in fact, what was often heard back then; but, I would wager that composers back then often cringed and wished that the playing were more refined.
****Why isn't all, or at least most, Classical music played on the instruments in use when the music was first written and performed?****
Assuming the availability of enough period instruments (still intact) to go around (not a safe assumption), playing those instruments presents special challenges to players. These instruments were not fully developed design-wise with fewer (or no) keys or valves in the case of the winds. These same orchestral players would also need to be ready to play more contemporary works that require the sophistication and more complete design of modern instruments without which much of the more modern (1800 or so +) repertory would simply be unplayable. It would be almost impossible for players to keep and stay up to speed on such a wide-range arsenal of different instruments for each historical period of music.