How? The most France could hope for was all the English Continental possessions. Edward III was a fairly legitimate claim to France, if Salic law is ignored. The House of Valois had no such claim and back in the middle ages, that's pretty damn important. Not to mention the logistics of Crossing the Channel with enough troops to conquer England, and getting the population not to revolt against them. The most France could do would be to put a puppet on the throne, but even then, deposing a Monarch outside of Byzantium at the time was essentially taboo.
No claim is strong unless it is adequately backed,and that claim,as it turned out wasn't.