Female pronouns are used to be gender-inclusive.
First off, singular "they" as a gender-less pronoun is not yet agreed upon as standard English again (see the next paragraph for why I used the word "again" here). It's cropping up more and more in spoken English, but is less common in writing, especially published writing (as opposed to communication such as email).
The use of "they" as a gender-neutral singular pronoun has a long history in the English language. It shows up in Shakespeare and Chaucer, for instance. In 1850, however, the English Parliament declared "he" to be the correct gender-neutral singular pronoun, and was largely successful at getting grammarians to back them.
Thus, for 150+ years masculine pronouns have generally been the default for persons of unknown gender in English. In the past few decades, feminists have begun to push back against this, with attempts at finding pronouns that don't assume unknown persons are male accelerating over time (which is part of why singular "they" is becoming a thing; the rising public awareness of persons who do not identify with either gender is also a factor). If you look at slightly older RPGs (e.g. D&D 4e, 13th Age), many use "he or she" everywhere to avoid specifying a gender.
The RPG hobby in particular was heavily male-dominated when it began. As RPG publishers have come to see the value in attracting female participants (both as players and GMs), they have tried to make their books more inclusive in an attempt to expand their customer base. Another example of this trend is the shift away from art depicting scantily-clad women being rescued by all-male parties, which was not uncommon in RPG manuals of the 1980s and early 1990s.
Using female pronouns for readers of RPG manuals is an easy way to express that it's perfectly normal/OK for women to play/GM RPGs. I have never seen any evidence of this being a negative for male readers of these manuals, who generally don't have trouble envisioning themselves participating in RPGs (since, again, the hobby has been male-dominated for most of its existence). Paizo uses female pronouns for its female iconic characters; per their creative director a desire to address inequality is a significant factor in that. White Wolf and its offshoot Onyx Path have been particularly up front about their desire to make their games inclusive. If you go looking for examples, you can find a lot of women talking about how this stuff really makes a difference to them.
Some rulebooks even explain this directly in the text. From the All Flesh Must Be Eaten core rulebook, p19:
Every roleplaying game struggles with the decision about third person pronouns and possessives. While the male reference (he, him, his) is customarily used for both male and female, there is no question that is not entirely inclusive. On the other hand, the "he or she" structure is clumsy and unattractive. In an effort to "split the difference," this book uses male designations for even chapters, and female designations for odd chapters.
Of course, some publishers disagree with this change and still use masculine pronouns, and, as above, a few will directly tell you why they're doing so. From the CthulhuTech core rulebook, p13:
Okay, here it is – we use he, him, and his when we’re talking
about people playing the game. It just seems weird to alternate
pronoun genders within the same book – it makes it feel like
the book is written for two different audiences. The masculine
pronoun is the standard and right or wrong we’re used to seeing
it. It may not be politically correct, but you can’t please everybody.
As for why English-language RPG books are doing this but French-language RPG books are not, that's harder to say. One possible factor is differences in how "correct" usage of the language is defined. The English language has historically been heavily on the "descriptive" side of defining language (especially in the US, and especially in the past 50 years or so); if enough people use the language in some way, then that's correct English. The French language, on the other hand, has tended towards being defined "prescriptively"; the Académie française is officially and legally in charge of defining what is, and is not, correct French language usage. This may make French language publications slower to change existing trends of pronoun usage. Additionally, French is a gendered language (i.e. all nouns have a gender), while English is not. Another possibility is that the feminist-led drive to question the "default masculine" in the US has not taken hold to the same extent in French-speaking nations.