Lucky nations do receive reduced AE.
You didn't actually read his post, it seems. He said that when he played as France, the results were cardinally different compared to when AI played as France.
The only difference here is France being controlled by the player vs France being controlled by AI. And this means that AI is treated differently by the game than the player.
The player doesn't get the lucky nation bonus, which is why you'll see more AE playing as France than the AI gets (25% less).
Is there a way to set up a mock battle? I want to pit 2 armies of exactly the same units against each other, right down to the same prestige, legitimacy, and power projection.
I wouldn't recommend going through the work to set this up, since the only modifier that affects combat that isn't visible directly from the battle screen is combat ability (and that is a rather minor stat). You can see exactly how prestige, army tradition, and power projection affect morale by mousing over it, in addition to all the other bonuses. Keep in mind that if there are multiple nations on one side of the battle, it'll list some bonuses separately (which is rather confusing) even though they are on an individual unit basis.
Morale damage done is based off of maximum morale, whereas unit damage is increased by discipline and combat ability (as well as dice rolls, unit pips, and leader values). If you have less maximum morale than the person you're fighting, you must have some combination of better composition/numbers or unit damage to win, period.
Since morale is so important early game, the big things to look out for to avoid being caught off guard and losing battles are national ideas, religion, and defensive ideas. Muslims can get up to 10% from piety, and Shia, Vajrayana, and Shinto get +10% as well. Defensive ideas give +15% and loads of army tradition (typically enough for around 5-10% more, this is true of offensive as well), and defensive and offensive both have events that give +15% as well ("relentless drill" and "full elan", very horrible to see). National ideas can be easily checked by mousing over the light bulb on both the province and diplomatic windows, but ones to remember that get morale early are Castile, France, Brandenbarf/Prussia, Persia, and Austria. Other surprises are morale advisors for +10%, or if you're really unlucky, an additional +10% from the level 3 morale advisor event.
Generally the player with a better composition, better planning/positioning, and the morale advisor can overcome even Prussian nonsense (well, maybe not the Prussians) without needing military bonuses or even a general. If you're losing battles unexpectedly due to their total morale being higher, these are the things to look out for. Later on in the game cannons and discipline become more important than morale, but fighting with a morale disadvantage will always be difficult. If you don't want to have to care about any of this, just take defensive ideas and you'll win most early fights without much care needed.