In addition to what we discussed on Discord, the only other potential issues that I've found are related to the army, and to be clear - they are based on my understanding of the army from reading your app, so it might be that I've misunderstood something.
The standing army of the realm is alright. Standing armies were not the norm at this point in time, but it's alright. France after all had the compagnies d'ordonnance, and later on the gendarmes.
The armies of the Kings are however a bit too much, but that depends on a few factors. The kings having their own retinues/regiments would not necessarily be an issue, like the gendarme companies, even though those were paid for by the King, who paid the magnate to raise the company. Who pays for the soldiers of these armies? The Realm provides the weapons, but who provides their wages? How large are they, in comparison to the standing army of the Realm? Because the text could also be interpreted as if each King has their own standing army that's of equal size to that of the Realm, and that's problematic. If by analogy though, each King has its own gendarme company, it might work, but even so, 2,200 lances in a gendarme company times 73 kingdoms is 160,600 - which is way too large for a standing army. So it's more likely that these groups are more like small retinues, with perhaps some of the smaller kingdoms having larger forces.
Furthermore, if each King has their own regiment, even just a regiment, how does the Realm keep their loyalty, and prevent rebellion? Who pays their wages is extremely important.
And there is no obligation to provide any numbers, but if you have a rough idea of the number of troops Gaul would have in total that would help me better imagine this - but I would really not want Gaul to be military stronger than France which was already a huge European military power at this point in time.
As for the peasants, again it's an issue of scale mostly, since I'm not sure what you're imagining. Having a reserve of free peasants who receive old weapons/can acquire their own is alright, as is them training in winter. The peasants being a problem is something that you have correctly mentioned, but if you're also teaching them war tactics, then peasant rebellions should happen a lot more often.
But their numbers would be limited. The role of peasants in agriculture would still be a lot more important than their potential as recruits. Even states that were existentially threatened and which made use of free peasants, like the Romanian principalities, only considered using some of them. There is also of course the eternal opposition of the aristocracy, which would fear the arming of peasant with war arms - and existential threats and a siege mentality can only do so much.
As for women in the military, I can concede the existence of some women among the peasants who train- I know of examples of Celtic women training and fighting in some situations, and there could be even some who fight, but accepting women in such a militia force in general is way too progressive for the era we're in.