Évreux may have a strong claim, but the daughter of the French King has an even better one. Claims are irrelevant anyways, given that French Princesses have absolutely no succession rights to give. But when it came to signing the Treaty of Troyes and ending that phase of the Hundred Years War, Henry V's marriage to Catherine made perfect sense and had propaganda value. Any other marriage does not.
The only way I could see Henry V marrying someone other than a French Princess (that is, a daughter of Charles VI and Isabella of Bavaria) is if something happens that Henry V chooses a more peaceful route and avoids breaking the twenty-eight year truce that had been signed in 1396 (unlikely) or Henry V's forces are defeated in France (which is probably even more unlikely).
Not saying he can't marry Blanche... but you need a scenario where it makes sense. He's not going to defeat the French at Agincourt, force the Treaty of Troyes upon them, and then up and decide to marry Blanche of Navarre, even with the Évreux blood in her veins. This is like Henry VII defeating Richard III at Bosworth, but instead of marrying Elizabeth of York, he decides to marry a continental princess because she has some Plantagenet blood through another ancestor.