I think the details of John's escape are important to how ATL plays out. If he manages to escape unscathed and tell this tale of an attempt on his life, then I'm not sure how much it changes the direction of the Burgundian cause. There was so much propaganda being pumped out by both sides that the Armagnacs could just say he was making it all up and the civil was just continues, with England playing each side off the other as before.
If John escapes but bears some obvious physical scars, like he's lost part of his hand after being attacked by an ax, then I think this event could be very seriously weaponized by the Burgundians to rile up north of France against the Armagnacs -- including possibly attempts to disinherit the dauphin, which rather indirectly buoys England's position since the next in line (via the Valois succession) is the duke of Orléans, who is an English captive, or an open Anglo-Burgundian alliance, like we saw in OTL. (Though perhaps one sealed with a marriage between Henry V and a Burgundian girl instead.)
If John escapes, but manages to wound the dauphin, then it's the Armagnacs who could perhaps try to make this a bit of propaganda about being set up.
I would also point out the most powerful family in the armagnac faction after Bernard VII's death was the house of Valois-Anjou so we can see definitely John or Philip conquering Lorraine and Bar from the house
Maybe on paper, but the Angevins were in a pretty sorry state. Marie of Blois, widow of the first duke, mortgaged basically everything they had in Anjou and Maine in the 1380s to try and fund the war in Provence, but her son, Louis II, was a weak figure who was never able to leverage Charles VI's madness to line his own pockets as his cousins did. (But he at least manage to
not lose his mortgaged lands, which is something.) Louis II's son, Louis III, is the poorest duke in France as a result. More importantly, the greatest piece of his patrimony, Provence, is under threat from Alfonso V of Aragon at the time of POD. It's not until Louis III makes peace with Alfonso and Joanna II of Naples in the 1420s that he becomes a major player in the Armagnacs. All of which is to say that Burgundy can just ignore Anjou for many years to come, unless somehow Aragon and Naples go easier on him in ATL.