Female perspective here! (The first paragraph is the most fundamental part of my answer, about creating a strongly written female protagonist. Also refer to Chris Sunami's answer and links. The rest focuses more on portraying a female character, or character of any marginalized group, in an authentic manner.)
Your female protagonist is the hero of her own story. Write her that way.
If you are in your character's head, you must write her as the baseline of her worldview, just like you would for any male character. This also goes for having a racially marginalized character, as yours is. She goes about her day just like a man would, and most of her thoughts have nothing to do with her gender or her race. She problem-solves and accomplishes routine tasks just like everyone else might. She has her own tastes and her own goals, and she can be selfish or introverted or musical or funny, just like any protagonist with XY chromosomes. She can enjoy interior decorating or hunting or video games. Let her be a person first.
To tie in with Amadeus' answer, make sure you aren't falling into the trap of ye olde stereotyped gender portrayal "Men act, women are". Male characters are usually given roles that drive the plot of the story, but too often female characters exist and have characteristics and follow routines but don't make meaningful contributions or have goals that are actualized as plot developments through their own agency. Make her and her wonderful brain essential to advancing the plot and resolving the crisis; she is an agent in your story, not an object.
Femininity vs. being female.
It's a bit unclear if you are having difficulty writing her as a feminine person or as a person who experiences society treating her as they treat women, but you can treat these as two different aspects of a character that are related but not an all-or-nothing bundle. Likewise, a person can identify with a certain ethnic group and may be treated as a member of that group, but there are levels to both of those, or a person can experience a disability that may or may not be visible to others or affect all aspects of their interactions with others. None of these are binary.
If she is "feminine" in your fantasy world, what does that mean? Does she conform to societal expectations for women? Does she spend more time with women than men, and do they bond over common interests? What are those expectations? What is normative female behavior? Like with men, this is a spectrum, and she can like pink and knitting but have no interest in babies and think cooking is less interesting than building robots. Treat it like your protagonist's tastes rather than her inherent personality. Note that most of what is "feminine" is strongly cultural rather than biological. Most people like being sexually appealing to others and make some effort to present themselves that way, but what is presented as feminine or virile or healthy or eligible can vary enormously by culture.
As for being a member of a marginalized group... The further from a societal norm she is, the more often and in more ways she will run into conflict with the expectations and discrimination of the majority/dominant view. The more she is forced to consciously confront and deal with societal marginalization, the more it will impact her life and worldview. Your character's goals are built upon a foundation of having the rights to life, liberty, and the pursuit of happiness. If she has these, she can go about building her life like any protagonist in a story. If they are lacking or impeded by societal bias, she will have to acknowledge that shaky foundation and either try to work around it by building a more precarious structure that defies societal expectations, or consciously fight to make her world better and more hospitable to her and others outside the norm and then build from a strong foundation.
So: if you want to consider your character as a marginalized person (especially in a fantasy society with rules you don't inherently know from experience), you first need to determine...
Exactly what is considered normal in this society, how much of a majority does does each normal demographic have, and how is it maintaining the status quo?
In our current western societies, men dominate the public sphere because it was traditionally entirely exclusive of females, and all of the norms are based on men and male expectations and male needs. There is entrenched resistance to change because when you have it all, change necessarily means ceding some amount of power and convenience. When accommodations have been made for women they've been implemented and often designed by men, sometimes merely paying lip service to equality and openness, and sometimes well-meant but lacking in practicality. Women have never made advances by asking politely; they have had to fight with all their numbers and political savvy and sometimes with bodily resistance to get what they need. This includes struggling against discriminatory hiring policies, sexual harassment, and even mundane details like repeatedly insisting that their workplaces stock personal protective equipment in smaller sizes. Ditto the able-bodied providing accessibility for those with disabilities, heterosexual rule-makers making accommodations for LGBT people, white people ensuring equal opportunities for people of color.
What is it like in your fictional culture? Just what percent of people identify as the majority for any demographic, and how oppressed are the minority groups? Has your society experienced any reformations or cultural revolutions? How recently? (Women are 51% of modern humans, but represented something close to 0% in public and corporate decision-making in 1905. Women were legally considered the sexual, economic, and reproductive property of their husbands in western society until scarily recently, 1970s in the US. Black people in the U.S. have been targeted for exploitation in as many ways as people could devise throughout history and still don't have enough legal protections to consistently develop financial security and generational wealth.) What rights are considered human rights, and what are regarded by the normative group to be privileges that can be withheld or rescinded? What methods are explicitly and implicitly used to maintain inequality and oppression?
What sets your character apart from societal normativity, and how would she experience these differences as external interruptions to her baseline worldview?
Her femaleness is not an issue unless someone or something about the world she's in makes it an issue. If sexism and misogyny are normal, your protagonist will not only have to deal with overt instances of it-- ones you, male author, can easily invent, recognize, and sympathize with-- but she'll also be sensitized to misogyny and feel a need to be on guard in situations where a male observer might not notice anything amiss. If this attitude is entrenched in her workplace, or her recreational haunts, or in places like parks and on sidewalks, it will color her thoughts and interactions. It's not about being feminine, it's about playing defense.
But there are so many other ways she may or may not match your own perspective! How are you handling these? Do they feel uncomfortable? How do these same questions apply to your male character?
This is exactly the same as above; just swap out race and racism. If you are constantly subjected to abuse, this will put you on guard all the time.
Remember, your character views herself as the baseline. Even if she knows she's the smartest person in her squad, she will still expect intelligent reasoning from the people around her until reminded through their actions or words that, in fact, people are dumb and she's an outlier. Others may look up to her as a genius, or the dominant view may be dismissive of nerds and wonks, or even hostile (think religious persecution of scientists). Does your genius protagonist have to watch herself?
Ethics, Values, Religion
If her ethical/moral/religious beliefs are not mainstream, she will routinely think of them as inherently correct and normal until something happens to remind her that people don't all think alike. If it's a constant bombardment (e.g., atheist in the Bible Belt), she'll be aware that she's at odds with others and guarded in her conversations.
Your character is not in the norm in terms of economics, but in this case it lends her more power. She has wealth, which makes her abnormal and perhaps hated, but in this case still more powerful than people in the norm. This power may shape your character's behavior more than being female, if your culture strives for egalitarian gender relations.
Side note: Effects of dominance vs. normativity
Note that if you are a member of a normative group you may be more likely to "flex" (show your strength or societal support) through microaggressions to exert your opinion, worldview, or desires in any given interaction, even completely unconsciously, without fear of societal repercussions on you. In my society, men constantly do small things that intimidate, belittle, or control women, even some that think of themselves as feminists, because it's an easy, sometimes totally effortless tactic to get things your way. Ditto white people with racial minorities, thin people to obese people. Microaggressions can be quite injurious, and those on the receiving end are often more aware of them than the ones doing it.
If you are in a position of dominance but not normativity, as with a person with substantial economic power when most people have far less, exerting your power gives you some control but without the inherent protection social approval, and may require a more strategic or tactful approach to avoid repercussions, especially if you are in other ways a member of marginalized groups.
Read female characters from female authors, and lots of them
I strongly support @Chris Sunami's suggestion of intensive reading of female authors writing female characters. While you're at it, consider their portrayal of male characters. Do they seem "off" to you? If not, it's probably because women are used to reading, sympathizing with, and considering the viewpoint of male characters as a normal baseline in all of those mainstream books by male authors. Thus, on average, they are much better prepared to write interesting and authentic male characters than male authors are prepared to write female characters. (Likewise, authors writing about any people seldom authentically represented in their reading material.) Immerse yourself in these books and characters. Try to get past the sensation of foreignness before you attempt to write in a similar voice.