The claim to the French throne by the English monarchs stems from Edward II's marriage to Isabella (the She-wolf to some) of France, daughter of Philip IV.
Philip III of France
Philip IV Charles of Valois
I I I I I
Louis Philip Charles Isabella Philip VI
X V IV = Edward II
I of England
John (Jean) I Edward III
The daughters of the sons of Philip IV were passed over, as the throne went (with the exception of Jean I, King in 1316) from brother to brother. With the death of Charles IV in 1328, the direct male Capetian line had daughtered out, and cousin Philip of Valois was chosen as the next King (reigned 1328-1350).
The contest really got into gear in 1337, with added friction between the
government of Edward III of England and that of Philip VI in Paris with
regard to Edward's lands in France. The claim of Edward III is technically based
on primogeniture, vs. the claim (in Paris) to adhere to 'Salic' law with
inheritance in the male line only.
Of course, in Plantagenet Poker, a few hundred cavalry and archers (with
a few thousand infantry) beats Dieu et Mon Droit. Not just a Highland
tradition: just ask Guillaume le Conquerant.