"In other words, can a war be just, and at the same time illegal? And if so, why not eventually recognize this contradiction, when facts impose themselves, why not look for reconciliation with belligerents that are not adversaries, in order to , together with them, commit ourselves to revise laws to make them once again coincide with good?"

Well one problem is the premise is wrong- assuming this is referring to Coalition vs Iraq. The war was not illegal. Nor if the US attacked N korea tomorrow would that be illegal. And this is for a very similar reason- N Korea has not ended the war it began over 50 years ago- but unlike Iraq, N Korea hasn't even signed an agreement ending the war- has simply ceased attacking until it decides it wants to fight again.
It takes two to fight; it takes two to have peace. Everyone would be quite happy if N Korea would decide that war was not a good option and pursue peaceful a relationship with S Korea. N Korea does not want peace. Iraq did not want peace.
But as to rest: "when facts impose themselves" meaning coalition forces are on the ground & controlling the ground, then unless you want to support forces opposing these forces, then it's a good idea to accept the "regime change". And Yes the US [and more importantly the UK] will work with France- we aren't going to trust them as much as we did before, but we do still trust them more than many other countries in which we are "working with"- Christ, it's "still" a democracy. And if France were to take steps which allow more trust, we are going to see this as a good reason to increase our trust.
And finally, because a war would be legal, does not mean it would be a "Just War"- currently beginning a war with N Korea would not be a just war- we most likely would not achieve a good objective- such as increase S Korea's security compare to it's relative cost (not so much money but in this case mostly S Korean blood). This equation would change if N Korea won't negotiate and continues to increasingly threaten S Korea and rest of the world. [The key to negotiating with N Korea is China- it's mostly a problem of their making- and they could- if they *really* wanted to- solve the problem. As a wild example, what would happen if China offered to put it's forces on the border with S Korea?]