In practice the Wars of Religion were indeed about religion which broadly speaking opposed Protestants to Catholics. But the origins of the eight wars reside in political conflicts. In three parts I will try to answer your question by first going back to the origins of the civil wars, then explaining the first three wars and their justification. Finally, we will se the last wars. As a side note and to be clear, I will use both terms, Calvinist and Protestant, but when speaking of Protestant I am referring to the Calvinists. Also, I set aside a lot of the international dimension of the wars. There is a TL,DR at the end.

The origins of the civil wars

If we generally pinpoint the start of the wars in 1562, we must at least go back five years earlier to identify one of the "point of no return". On the evening of the 4th of September 1557, a large group of Calvinists met in a house street Saint-Jacques in Paris. Neighbours found this large gathering suspect and informed the city watch. Many people were arrested. In itself, this mass arrest of 120 people or so was quite an event but the authorities were confronted with a new terrifying (in their opinion) problem: many of these Calvinists, especially women, were nobles. The repression against the Calvinist cult existed since king François I and continued under king Henri II. But in the highest spheres of both temporal and spiritual power, the extent of the "Protestant infiltration" in France was yet fully understood. Yes, there were heretics here and there and when necessary they were punished, forced to recant or executed when an there was a need to make an example. What the Saint-Jacques street event highlighted was that more people had actually converted to Calvinism than what was previously thought and these individuals were nobles. For king Henri and many others it was a shocking discovery. Eight people were executed, including a noblewomen like Philippine de Luns and one of the queen's former ladies, whose name I can't find back. Protestantism and nobility were the two ingredients that turned the Reformation in France into a political crisis.

From Geneva, John Calvin had in his mind to convert Catholics. After the event of September 1557, his objective was to make Henri II renounced his allegiance to the Catholic Church. An ambitious plan which he hoped to carry out by sending "missionaries" to the king's entourage. The first two targets are the Bourbon brothers, both Princes of the Blood (descendants of a Fils de France), relatives of the King. The eldest, Antoine, is King of Navarra by his marriage to Jeanne d'Albret. Perhaps he was already a Calvinist (his wife was) but he did not make it known until 1560. The King of Navarra was more preoccupied by personal ambitions and would not anger the kings of Spain and France just yet. In 1562 he was once more Catholic. The youngest, Louis de Bourbon-Condé is a renowned warrior and commander who was easily converted, he became the leader of the early Huguenot. Other targets include the three De Coligny brothers. Gaspard de Coligny is the Admiral of France, François is the lord of Andelot and the third, Odet, a Catholic bishop. They all became Calvinists. There are numerous other examples. But what one needs to understand is that these are some of the most important individuals in the Kingdom. They have prestigious names, they are wealthy and the patrons of many lesser noble families that are ready to follow them, including in changing religion. Calvin didn't succeed but his hand reached quite close to the King.

The following years were more repressive than ever. Henri II wished to put an end to the heresy because the ideology of the monarchy supposed that every single subject of the French sovereign followed his religion. Heretics, especially in such numbers, were an obstacle to peace and harmony within the kingdom. In theory, the king was the "father" of his subjects, and "children" who had different beliefs than their "father" could not be loyal. Furthermore, the fact that so many nobles were now Calvinists was both terrifying and infuriating, a danger to royal power. The edict of Ecouen, signed by Henri on the 2nd of June 1559 is perhaps the symbol of this increased repression. It stipulated that any fleeing Protestant could be executed on sight, without any form of trial. Still, it did not prevent the clandestine French Reformed churches to exist. Henri died on the 10th of July after a jousting accident. His unfortunate killer, Gabriel de Montgomery, was a suspected Calvinist (and rightfully so as the future would tell). France was inherited by 15 years old François II. Weak both in mind and body, it was decided to create a regency even though François was an adult. Catherine of Medici, the Queen Mother, became Regent but in name only.

With the Regent sat the Lorraine brothers, François the Duke of Guise and cardinal Charles. Their faith in Catholicism is very strong, they hate the Reformation and wish to eradicate it once and for all. Their family is extremely powerful. They are uncles of Mary Stuart and played a part in securing her marriage to young king François II, in order to form a Catholic wall against England. They are powerful but they are hated in France. By some Catholics but mostly by the Calvinist nobility. The Calvinists hope that if the Guise could be dismissed from power then they could influence the young monarch to, if not convert him, be more "tolerant". In 1560, a plot was formed to take power off the Guise while they were in the Castle of Amboise. It was a complete failure. One plotter apparently gave the whole plan away while he was drinking in a tavern. Anyway, the Guise were well aware of the conspiracy and repelled the assailants after a small skirmish. The leader Jean du Barry was killed. The repression was horrifying, some were hanged, drowned, …Etc. None of the nobles involved in the conspiracy of Amboise were important, they belonged to the lower nobility. It is unclear if important nobles such Coligny and Andelot played a part, maybe they knew about it but did nothing. However, they were the culprits in the eyes of the Guise. Similar conspiracies happened elsewhere in France, most notably during summer 1560 in Lyon, when lower nobles tried to capture the city and install a "Calvinist-friendly" government. The only thing these conspiracies achieved was to enrage the Guise who suspected more and more the Bourbons and Coligny. On the orders of the Duke of Guise, Bourbon-Condé was arrested in the city of Orléans and sentenced to death. What saved him was the death of king François II in December 1560. The new monarch, Charles IX, was 10 years old and needed a real regency with his mother Catherine. She pushed the Guise away and released Condé. All this happened two years before the war started. Yet, the country was already deep in a political crisis fought between the nobility. However, individuals on both sides still hoped for a peaceful settlement. Catherine didn't wish for war but to keep the Kingdom united for her sons. Around her gathered moderate Catholics, called the Moyenneurs. They were not necessarily tolerant (in the modern sense of the word) but knew that the situation had to be resolved peacefully to avoid a civil war. On the Huguenot side, Gaspard de Coligny hoped the King and Queen Mother could be convinced to stop the persecutions and grant them freedom of worship.

The Calvinist churches beneficiated from a strong and well organized network, especially in the South of France (the Presbyteral polity). They elected representatives and sent them to the King with petitions. In 1561, it was agreed to organize discussions on the issue. The colloquium of Poissy is one of those with Catholic bishops, pastors and theologists such as Theodore Beza trying to find a solution. But both sides wanted things that the other side could not agree on and it was a failure and no religious coexistence was achieved. Though still at peace, both sides were being more and more anxious about the prospect of an open conflict. The Catholics were the first to organize themselves as a political "party" of sort with the Triumvirate. The triumvirs were three staunch Catholics, all soldiers: the duke of Guise, the Marshall of Saint-André and Anne de Montmorency. They put pressure on Catherine to resume the persecutions. She resisted them and tried to find, if not a religious coexistence, a civil coexistence. She passed the Edict of January in 1562 which granted the Protestant the right of worship outside fortified cities and the right to use hospitals, to access offices. Fervent Catholics were furious. France was a keg of powder, it just needed a spark.

The spark fired on the 1st of March 1562 in Vassy (or Wassy). François de Guise was on his way to Paris with his family, returning from Lorraine. Near the small fortified town of Vassy, someone told him that Calvinists were praying inside the walls. The Duke sent men to investigate, all too happy to find Calvinists breaching the law. The situation escalated and the Duke's men ended butchering around 50 Calvinists. This event happened by luck (for the Catholics). It was chance that made Guise ride next Vassy and chance that made someone rat the Calvinists. But for the Huguenots it was a deliberate action, a conspiracy by the Guise and as the war was finally starting they became a true, organized, political faction/party.