Matteo, I do not disagree with most of what you said, you are even mostly right but a couple points.
1) Edwards claim while serious in law, was not serious in fact, but legally he had as good a claim as anyone.
2) After Charles IV death the peers had an informal and illegal election (it was not formal) that is why they made up a law and said it was old and fundamental. Which they had no legal right to do, they were not regents or kings. At most this adds moral right to the valois claim, not legal weight.
2 and 3) You could argue that childhood inheritance at that time only applied to the sons of the king, and that is why or part of the reason Joan was passed over for her uncle. Since minor daughters of the king can not inherit then the minor descendants of daughters can't either. No real precedent but nothing against it either.
In practicality you are right and morally you are mostly right too, but legally at that time, the laws of succession were just to ambiguous to dismiss Edwards claims on legal grounds. Unless you illegally and immorally make up laws to hide the fact you had an illegal election.
1) A very good one, yes. But not the best in a coherent system, be it Salic Law, women's ability to reign or women's ability to transmit the crown to their son without being allowed to reign.
3) That's what you would want to argue but that's not what the nobility would have argued.
As I already stated, the french crown was not a fief. Not was it a private property.
The only legal point was that the crown had been elective for around 700 years. And that there had been a customary evolution with Philip II Augustus : the rule of election being shelved because of the overpowering prestige, wealth and political strength the Capetian kings had acquired. But it could be réactiva terme as son as the political situation made it necessary again.
Your hypothesis that only sons of males could inherit when still in legal minority is groundless and it was never put forward but the contenders.
Let's just imagine that it had been put forward by Isabelle in d'avoir of her son Edward. The likely reaction would have been a mix of laughter and outrage, and some answer like : "Someone who is under the guardianship of the foreigner lover of his mother can not be elected king of France since he de facto does not enjoy the enjoy the rights of civil and legal majority."
As I stated, Edward could have the right argument for contesting someone else's election but he could not find the right argument for having his candidacy considered as the most legitimate. Things would have been different if he had been married to his cousin Joan of Navarre.
His only way to have his candidacy backed by a majority was in the political field. Bad luck : the french nobility did not want a Plantagenet king of England.