I don't think that the Haspburg could have inherited the French throne.
For one, there is the French Salic Law : it excluded every female and their bloodline from the succession. This had been done first in 1316, after the death of Louis X and his posthumous son John I, to prevent Joan of Navarra to succeed the crown as they were doubts on her legitimacy and also fear she could have married a foreign prince. That's how Philip V, Louis X's brother, got the crown.
Since Philip V died in 1322 without any male heir, the succession went to his brother Charles IV who in turned died in 1328 without any male heir. That's when Isabella of France, mother of Edward III, tried to assert her sons' rights to the crown saying that, though she herself couldn't inherit, her son could as he was male. The French didn't want an English King on the French throne and so the crown went to Philip VI, a nephew of Philip IV and a 1st cousin of Charles IV.
There is also a technical fact : some of the daughters of Louis X, Philip V and Charles IV had married and has sons themselves who would have had more legitimacy than Edward III but who could also have claimed to have been usurped French Kingship under the rules of Philip V or Charles IV (a claim that happened OTL with Charles II of Navarra, the son of Joan and her cousin Philip of Evreux and thus the grandson of Louis X). It would have ended in quite a mess...
When I learned about Philip II of Spain's attempt to have his daughter Isabella as Queen of France, I was surprised as, to me, it wouldn't have been possible as it violated the French Successoral law. I'm not sure he had any chance to suceed, even with brutal force. This might have lead to a "Hundred Years War" between France and Spain, but I don't think it would have resulted in Isabella being crowned Queen, or at least there would have been a rival and legitimate King for the French (Henri IV).
Second, the Hapsburg aren't a male branch descending from the Capetians, like the Valois and the Bourbons were. They do have French blood in their veins since Maximilian I had married Mary of Burgundy, daughter of the Duke of Burgundy Charles the Bold, who himself was a descendant of the French King John II. Yet, it is a female bloodline and thus excludes the Hapsburg from the Succession.
Besides, even if the Hapsburg were male-related to the Capetians, they would come after the other French Branches. The Valois were descendants of Philip IV of France's brother, Charles of Valois, meaning there bloodline descends from Philip III. As for the Bourbons, they were descendants of Robert of Clermont, one of Louis IX/Saint Louis's son (the youngest if I remember correctly). Unless the Hapsburgs could prove to have a stronger blood link to the Capetians than any other candidates, they wouldn't get the throne.
Third and last, the French didn't wish for Foreign rulers. That's why we got the Hundred Years' War : because Edward III of England could have claimed the French throne, the nobles choosed to ensure Salic Law by forbidding women and their bloodlines to succeed the French crown. The Haspburg are partially French since they descend from Charles the Bold but they would look nothing but German (or Spanish, depends on the candidate) to the French people.