This AHC is tricky because IMHO what would have been best for France during the reign of Louis 16 was not the stuff of "greatness", at least not when we consider traditional/popular historiography. France didn't need more Louis 14/Napoleon-esque wars of conquest/gloire (which it wouldn't have won anyway); what it needed for its long-term prosperity was peace, internal reform, economic development, and international markets.
Even then, 16's freedom of action would have been constrained by phenomena beyond his control. Financially, Versailles' freedom was limited by debts and a high rate of interest on loans. Politically, even assuming 16 doesn't reinstate the parlements, he would still have had to walk a delicate path between triggering 1 + 2 Estate or 3rd Estate opposition. Bureaucratically, the sweeping reforms of the Republic/Consulate/Empire, and the Enlightenment-era talent that implemented them, would have found their work much more difficult in aristocratic Versailles. Diplomatically, 16 had very little chance of gaining political capital/gloire through war without triggering a larger European conflict, thanks to the alliance systems on France's borders. On an ideological level, absolutist Versailles was not exactly the most fertile ground for conceiving/implementing internal reforms, and neither was Louis XVI on a personal level.
A Louis XVI that worked in France's best interests would probably have a historical assessment like: "he effectively managed France's transition from absolutism to constitutionalism", which while extremely important doesn't exactly scream "greatness". But to achieve that, I can think of several things he should do:
- Foreign Policy: actually quite OK OTL - general peace, rapprochement with Britain (Eden Treaty) except in cases where victory was pretty much guaranteed (American Revolution). Not much change here, although a longer-surviving 16 would probably have had to manage revolutionary movements in other countries (Netherlands/Austrian Netherlands esp) and eventually, the likely dissolution of the Spanish colonial Empire. Perhaps France could have been an early proponent of the Congress System.
- Political Policy: to actually carry out internal reform 16 needs political freedom of action and that absolutely means NOT reversing Maupeou's 1771-4 effort to destroy the parlement of Paris. However, given that raising revenue will be a foreseeable problem in the future and the French Army OTL failed to suppress rebellion/disobedience, it's probably best for 16 to get ahead of the problem and start a controlled transition towards national political representation. Maybe the sort of gradualism that Napoleon III did.
- Economic Policy: abolish internal + feudal tolls, rationalize taxes, invest in infrastructure, promote international trade via diplomacy or military.
Looking back, this list sort of resembles what Napoleon III did, hopefully minus the costly foreign adventures.