Even a military victory by the Huguenots over the Catholic League would not give them the power to impose their power on all of France. Nonetheless, a Huguenot victory is certainly possible, and there are several possible PODs that would allow that. The easiest, off the top of my head would be for Henry Bourbon to either remain a Protestant, or for his Huguenot supporters to make it clear to him that they will not accept his conversion to Catholicism without regarding him as a traitor to their cause. Even as late as 1593 Henry's military situation was perilous, it was mostly the inability of his enemies to unite around one candidate that prevented his opposition from becoming very organized. If the League had accepted Charles de Lorraine as its candidate for the French throne, Henry could very well have decided it would be militarily impossible to abandon is core constituency.
Now assuming Henry can defeat all his rivals in the field, he would still have to take Paris to be considered King of France. The city would never open its gates to a Protestant, so he would have had to initiate yet another siege of the city in 1594 or so, and hope that the Spanish are too preoccupied to relieve the city. Paris would be starved into submission, but still require a large garrison. Henry would next have to conquer Brittany and Provence from the League, difficult tasks because of those provinces proximity to Spanish power.
Once these military victories have put Henry on the throne, he has now put himself in the approximate position of James II of England. He will be a religious minority attempting to impose political absolutism on a country that largely opposes him on religious grounds. Oh, and he will have deprived his dynasty of the aide of several skilled Princes of the Church. In return the Bourbons get to be the champions of Protestantism, and condemn themselves to be dragged into wars with Spain and the Empire attempt to assert their authority over the Netherlands, or Germany.
What would really interest me is how this would affect England. What if Britannia's mortal enemy was Protestant, not Catholic France? Could the historic enmity between those two countries be healed in the 17th century, or would their rivalry become an embarrassment to Protestantism the way the conflict between Denmark and Sweden war?