Well . . . depends on what side of the Channel you were sitting on. Edward III (of England) was indeed the grandson of Philip IV of France (Ed was Phil's daughter's son), but Edward would never have been considered King-of-France material if the Capetians had been able to produce a male heir. Considering the ongoing state of tension between England and France at the time, it was unlikely that the French were going to accept an Englishman as king of France. I don't know how seriously Edward took his theoretical claim to the throne of France, but it was a good enough excuse to get a war started.
And I'm sorry, but Joan is just way cool.
That's right....if. But the Capetians didn't have a male heir and the law on both sides of the Channel as you put it was that Edward had the right to be king. Of course then it was inevitable that he would claim his rightful throne; even the previous King of France had named him as his heir.
The French flouted the law which is why I say their current love of lawlessness and just doing what feels good might be traced back to this time.
Joan of Arc? Think she's a bit flaky myself. But a lot of people thought she was "way cool" back then too which politically is why the French used her rather than abide by law.
Since that time, the English have been known to be more enamored by the rule of law than the French. The frenchies still have trouble enforcing the law today as we all know.