Well, this former Protestant will echo your "French" in saying that they bloody well succeeded!
Some might say this was the goal of the reformers, some might actually believe it to be a noble thing, unity and all.
Some others say the goal is far more sinister. Some others say that the source of grace in the world is The Catholic Church, primarily through the Holy Sacrifice of the Mass, the sacrifice of Calvary, offered by the Catholic priesthood. Some might say that Satan knows this, and since he wants to bring as many souls as he can to hell with him the three big targets he would want to attack would be The Church, the Holy Sacrifice of the Mass, and the priesthood.
Some might say that although the Protestant revolt did do damage to The Church, it would be far more effective if the attacks on the Church could somehow be made from the inside. So, some might say, Satan went to work attacking the very means of grace, the Sacraments of the Catholic Church, (primarily the mass but all of them have been changed including Holy Orders). Some might say to do this he would need accomplices, no problem with that, he would only need a few. The vast majority of support he would get would be from those who serve his purposes unwittingly under the belief that they are really doing good, you know unity and all.
Anyway, Satan doesn't care if everyone feels good about being united so long as they are united in error an confusion and not truth. And isn't that just what has been accomplished. Less Catholics going to confession and mass on a regular basis, less Catholics believing in the Real Presence, less faithful priests teaching orthodox doctrine, less valid masses, and more flexibility to have masses that profane the Eucharist and foster something other than the Catholic faith, less grace for the world, less divine protection against sin and error, and a whole lot of souls being lead astray. And most of them feel really good about it.
Anyway that's what some others might say.
Oh, go on! Beat about the bush if you must! ;)