This doesn’t seem to make a lot of sense when you consider the fact that women were seen as less intelligent and weaker than men during these times and wouldn’t even have the right to vote in the US, U.K. and France until the early 20th century.

To go broader than your immediate title question ... the issue is a lot more complicated than "men were considered strong, capable, and smart and women were considered weak, incompetent, and stupid". As I explained in my answer to Were there women opposed to suffrage?:

Basically, by the 1840s, it was firmly established that men and women were complementary in all things, and that while men had to go out into the world to make money and participate in politics, each needed to be balanced with a sweet woman who took pride in domestic management and raising children, on the personal level as well as on a macro scale. (This ties in very strongly to Queen Victoria's self-presentation as the mother of a nation/empire.) Today we recognize that this is an unfair playing field, and that men and woman should be given the same opportunities and expectations, but the complementarian view was very widely held by both men and women and was generally put as a positive: women were morally pure, and by raising children and creating the ideal home for men, they were influencing the world on a much deeper scale than any MP or senator who made laws or a random male citizen who cast a vote. The nitty-gritty of politics was opposed to this moral purity, and, it was thought, could muddle it. Women who took on masculine qualities or tastes weren't bad, per se, but they were unnatural and a threat not just to their individual family, but also on that macro, societal level - including to other women, since their own high moral standing was derived from everyone believing that their domestic duties were as honorable and worthwhile as men's public work that earned money. All of this is very middle-class, since it relies on a male-wage-earner/stay-at-home-mother pairing that didn't exist among the working classes (where women often had to work for a wage or at least concentrate mainly on the onerous and dirty work in the home, since they were unable to delegate it to a servant, and not spend hours reading to and instructing children gently) or the upper classes (where men often didn't earn a wage, but lived on inherited money, and wives had access to lots of servants to handle domestic management and childrearing) - but the limited applicability in some sense strengthened the power of the ideal. Working-class women saw it as a life to be aspired to, and used the stereotypes of female innocence as their one defense in court or in public life, for instance.

Historical fiction written in the later twentieth and twenty-first centuries tends to take our modern consensus that this is unequal and unfair treatment and project it back, having only bad characters believe in it for the most part, and having any good male characters stop believing it promptly after seeing evidence of female competence. The bad characters do not really believe in the beneficial qualities of women, too - they use this philosophy as an excuse to marry women against their will, imprison them in asylums, steal their money and property, etc. And certainly many men historically did this as well, but it was by no means all a pretense. Women were seen as possessing good qualities of their own, and if they appeared to be doing something coded masculine well, it was always possible to show them as exceptional examples ("Most women don't have much of a head for mathematics, but you wouldn't believe what Miss Lovelace is working on!") or, in extreme cases, redefine the coding.

The concept of depicting a people (in the sense of an ethnic group) as a woman originated with the Romans, and was revived in the Renaissance/Early Modern Period for self-description by a number of countries - Britannia, Dame Scotia, Helvetia - and in Early Modern art there's also quite a lot of female personification of various virtues, sins, and abstract concepts. Portraying "liberty" as a woman, as revolutionaries in France were doing from the 1770s on, was simply traditional, and also allowed the supposed moral superiority of women to be brought into play; most likely the ideal of protecting a woman or womanhood with violence also comes into it psychologically, as artwork and rhetoric that made the country or the revolution or the quality feminine could be seen as exhorting specifically men to come to its aid through war. The famous painting by Delacroix certainly shows Marianne as more active on the battlefield than others might, but she's also holding the gun rather than firing or even brandishing it, her more engaged arm holding up the French flag that she also represented. The Statue of Liberty comes from the same tradition of anthropomorphizing liberty and doing so with a woman's form (it's a French artwork given to the US), and likewise she's not performing any kind of violence or direct action: she's holding a torch and welcoming the huddled masses - it's somewhat maternal.

I hope this makes sense?