Why did England allow women to rule as queens in their own right since the beginning of the monarchy despite the usual societal views of the role of women, and how did she command respect and authority in such a patriarchal society? by u/Gnatlet2point0 goes VERY in depth on the history and events that precipitated Elizabeth I taking the throne in England. Unfortunately it doesn't discuss much about other nations.

I can address the case of France.

Until 1316, no woman ever became the queen of the Franks/of France (outside of consorts). This was due to a very simple fact : there was always a male relative to succeed the king when he died. There was always a son, a brother, a nephew or an uncle who had a legitimate claim to the crown, and who would always be chosen over a woman, and in this the Frankish/French monarchy was no different from any other in Europe. England for example had no ruling queen before Mary I in the XVIth century. Of course, women would exert power, but always through underaged son, or temporarily absent husbands.

In 1316, Louis X died, leaving his wife pregnant with a posthumous boy, John, who was crowned king upon his birth but died just 4 days later. Louis also had a daughter from a first marriage however, Joan. It was not completely unimaginable for her to ascend to the throne; there was at this point no clear successon law within the monarchy. Contrary to popular belief, the Salic Law was absolutely not invoked by contemporaries, nor was it even considered relevant at all : it dated back to the VIth century, some eight hundred years prior to this, and was thus not applied anymore. In fact, most people, included the educated ones, probably didn't even know that it existed. It is only retrospectively, in the XVth century, that Salic Law was used as an argument to reject the english claim to the French throne.

In 987, Hugh Capet was elected king of the Franks, inaugurating the capetian dynasty. For more than three centuries, the family was blessed with incredible biological luck : there was always, like systematically, a son to succeed the father on the throne. From Hugh to Louis X, there is an unbroken line of succession from father to son. However, Louis, and then his son John's deaths, created an unprecedented problem. This time there was no blatantly obvious and undisputed heir to the throne. Still, the crown passed, without a real debate, to Philip V, brother of Louis X. He had already been regent of the kingdom for several months (as John was born after his father's death, creating a short period of interregnum), was son, brother and uncle of king, and had the support of the nobility. His only "rival" was Joan, the only other child of Louis X. However, she had several things stocked against her : being only 4 years old, being born of a mother who had had an affair with another guy for several years and was subsequently repudiated, which made many doubt if Joan was truly Louis X's child, and she was a girl. This was not a problem only because of the misogyny of the time, but also because being a woman meant that you would marry someone. Thus, Joan being queen of France meant that the kingdom would find itself with a consort king, and nobody liked the idea. What if the husband was a foreigner, whose house would take over France through this marriage ?

Philip of course, as a capetian prince, was the last person on Earth who would let that happen. He thus basically staged a coup, had himself crowned king and put what few supporters Joan had before the fait accompli : he had been regent since Louis' death, he was now king, what were they going to do ? Would any noble seriously think of starting a civil war for a 4 years old girl with doubtful legitimacy ? Well no, nobody did. Philip V quickly gathered the Estates, which argued that as a brother of Louis X (and an uncle of the short-lived John I), Philip had precedence over Joan to inherit the crown. The same process repeated itself in 1322 : that year, Philip died, having produced only daughters; the third and last brother of the family, Charles, evicted his nieces and was crowned king, based on the precedent established in 1316. Once again, nobody objected. There was no need to invoke a Salic Law, whose existence had long been forgotten at this point. It had simply been agreed on, through a coup in 1316 and another in 1322, that the crown should go to men rather than to women. So when Charles died in 1328, the situation became a bit confusing. Charles only had daughters; however, his wife was pregnant. So if she gave birth to a boy, he would be king. If it was a girl, the moribund king said that he was letting his barons decide on what to do.

Here's a family tree, it's soon going to come in handy. On his deathbed, he also appointed a man to be regent for the period between his death and his child's birth : Philip of Valois, son of Charles of Valois, himself brother of Philip IV, father of Louis X, Philip V and Charles IV. Philip of Valois was thus the first cousin of these three, and when Charles died, he became the eldest member of the capetian dynasty. He was 35 years old, quite popular, and, if Charles' posthumous child happened to be a girl, he would be the eldest of the male line descendants of Hugh Capet... which is exactly what happened. So without surprise, he became king Philip VI in the spring of 1328. There was some protest from Edward III, son of Isabella, herself daughter of Philip IV and sister of the three brother kings. This would play a role in triggering the Hundred Years War, but in the end the house of Valois prevailed and eliminated any opposition. To rule out Edward III and the entire english royalty with him, the Valois kings formalized the principle that no woman shall inherit the French crown, or even transmit the right to inherit it, and they named it "Salic Law", after rediscovering its existence in the second half of the XIVth century.

So women were ruled out of the succession more due to circumstances (the need to render the english claim invalid), than due to some grand principle, which did not exist until well after said need emerged in the Hundred Years War. Still, it did not become completely unimaginable for women to inherit the French crown; after more than two and a half centuries of unambiguous succession within the house of Valois, a new dynastic problem emerged, as the childless Henry III found himself with no other heir, than Henry of Bourbon, who happened to be slightly protestant. The hardline catholics of the kingdom tried to find a new heir (or king, after Henry III's death) to impose by force, and when all other options fizzled out, some recognized the spanish infante, Isabella, granddaughter of Henry II through her mother and daughter of Philip II of Spain, as queen of France; however this went nowhere, partly because even among hardline catholics, only a few supported the idea of giving the crown to a foreigner, and partly because Henry of Bourbon, now Henry IV, gradually crushed or placated any opposition to his rule. After this, the throne would no longer face any similar controversy before the XIXth century, and even then, the inheritance of women was not the problem.

To put it simply : the French crown never went to a woman, because it never found itself completely deprived of any other potential male heir. Each time a woman came remotely close to inheriting the crown, a man with his own claim to the throne was able to rule her out. This is different from what happened in England for example, when the royal house frequently found itself running out of male heirs, leaving only women to ascend to the throne.