As soon as the civil war between Henri of Navarre's Huguenots and Louis of Guise's Catholics, the anti-French coalition collapsed, and different sides begun to support the two factions. Soon enough, actual intervention begun into French territory. Heavy fighting also spred, with time, to Germany, Poland, Italy, Castille and even Russia, Scandinavia and North America.
Not all the supporters of different factions were supporting them because of religion - first off, Huguenots were supported by the whole of Lisbon Alliance, including UPC and Portugal. The Lisbon Alliance was NOT interested in a strong France, but it felt that a civil war will weaken it, and a strong France friendly to the Alliance is better then a strong France hostile to it. Other supporters of the Huguenot France were the Denmark-Norway and the Schmalkaldic League, which, pretty much, was all of the Protestant Princes of Germany. At a slightly later point on, Russia got involved on the Lisbon Alliance side as well (OOC note - Time of Troubles is cancelled - Otrepyev gets no Polish support as Polish nobles have better things to do, like fight Turks. Boris Godunov dies much later then in OTL - probably as butterfly effect, but also there is much less stress when you don't know that there is a huge rebel/Polish army marching towards your capital).
Guise-supporters are pretty much obvious - Aragon, Jagiellon Empire, Bavaria (chief Catholic German power), other minor Catholics, Venice, the Papal States and the not-as-obvious Sweden for which it was an excuse for another war with Denmark-Norway.
Though there were less nations on the Catholic side, it was soon proved by the Polish forces that the chances were still pretty equal. The Guise Catholics were also somehow stronger then the Huguenots, even if marginally.
At that point, Jagiellon armies were fighting an on-and-off war with the Turks, and were on the defensive there, so they did not need many troops on that theater.
Very quickly, the Polish forces used this situation to annex their vassal in East Prussia on the account of planned treachery. Soon after, Polish forces also crushed a pre-emptive attack by Protestant princes at Warta and marched into Bradenburg.
In France the Huguenot powerbase was definitely the southwest, though Normandy at that point also was on their side, reinforced. If a bit reluctantly, the Italians supported the Catholics, as did Occitania (southeast) and the main area (north, minus Normandy, Brittany and Artois). In France, indeed, the fighting was perhaps the most severe - Schmalkaldic League, Lisbon Alliance, German Catholic, Venetian and even Papal forces were fighting throughout it, looting and pillaging as they went. The war hung in the balance there, as Henri was a more capable commander then the numerically-superior Louis.
War was also fought in Italy, on the western Russian border (Stephan lived longer in Poland and gained Smolensk ahead of time), on the sea and even in North America where a Dutch expedition in 1609 almost succeeded in taking Christinaburg.
As said before, one of the opening moves of the war was in Germany, as Polish forces, deciding to take out the major Protestant princes one by one, crossed the Oder after the victory at Warta. The Polish forces, led by Valdemar Bathory, plunged into Brandenburg, and by 1605, they held Berlin, Magdeburg and Dresden (though their control of the countryside was minimal). Attempts to advance to Mecklenburg and link up with Sweden failed due to the determined defense there, assisted by Dutch, Danish and English forces. However, they did link up with German Catholics and soon threatened the Palatinate. Unfortunately, Louis failed to commit enough forces to break through at Rhine and lost the Battle at Disentis against the Palatinate of Pfalz. That came just in time with another major defeat in 1607, when Henri seized Rennes, linking up with Duc d'Bretagne - another Huguenot and Henri's brother (in OTL, he did not exist). Only the succesful occupation of Normandy in late 1608 somehow relieve the Catholic position. At that point, Venetian, German, Castillean and Papal forces were already fighting throughout Italy and France in series of skirmishes. In Spain, the Castilleans led by Fernando Malingi fought back the Aragonese offensive at Murcia.
Perhaps one of the most crucial events in the war came in 1609, when Boris Godunov decided that the time was ripe. In the days of Ivan IV, Russia was in very good diplomatic relations with England, and Godunov intended to exploit it in the future. He was aware that Poland was fighting a two-front war in Germany and Hungary. Besides, he did some army reforms - though Russian army still was rather... primitive, it was better then in Livonian War. And, finally, Godunov worked on establishing contact with potential Cossack rebels. The latter did not suceed in raising a rebellion, but the possibility of it remained. Nevertheless, the undergarrisoned Polish eastern border was attacked by streletz troops, whose numbers overwhelmed the garrisons with shocking ease. Sweden, oddly, was not attacked and thus it managed to rapidly seize Pskov, cutting off the offensive into Livonia from Russia. However, the Muscovites seized Riga, Smolensk and even Kiev. Polish forces managed to stop the Russian westward attempt at capturing Minsk only in mid-1610, but there was no time to launch a counter-offensive. Godunov proceeded to personally retake Pskov after encircling and crushing the Swedish forces (despite suffering huge casualties, he could afford it) at Izborsk, 1611. Soon after, Russia made separate peace in Lublin with Poland and Sweden, keeping (out of their gains) Estonia (rest of Livonia remained Polish due to a succesful Polish counter-offensive there), Ingernia (OTL St. Petersburg region) and lands east of Dnepr, including Kiev and Smolensk (but excluding Minsk). For Godunov, that was a very important achievement, if only because Russia now regained access to the Baltic Sea, enabling its fur trade to rise again. Some doubt that it was a part of the French Succession War, but it most definitely had an effect on it.
With this distraction, the Polish offensive against rebels in Bohemia and German princes on the Rhine was cancelled. Newly-crowned Valdemar decided that time for peace has come in 1614, after Paris fell to the Huguenot forces. The following Treaty of Rome brought an end to a very bloody war which ravaged France and Germany alike.
The results were largely inconclusive in some areas. Bavaria was now the only Catholic German power of any significance, but it managed to annex some smaller principalities, so the hopes for an unified Protestant Germany came too early. Holy Roman Empire still "existed", but it was even more nominal then before. Aragon and Castille returned to pre-war borders, with Phillip II still brooding over the failure of reunification of Spain and the Castillians still wary over the hated Hapsburgs in Aragon.
What the treaty did achieve was the general calming down in Europe and decrease of religious tensions. It also broke French power for many years to come. French possessions in Italy were now an independant Kingdom of Italy (how ever loose and unstable), headed by Louis I Guise. Huguenot faction triumphed in the rest of France, and Henri IV (more rash and more Protestant then in the real world, but still a capable politician) established the Bourbon dynasty. Both France and Italy were now looking with interest at North America, but Italy would have some problems getting there - Lisbon Alliance holds the Straits of Gibraltar pretty well, as Portugal controls Tangiers and Castille controls Gibraltar itself.