Definitely sounds tricky! If there is still time to switch topics, that may be wise, however there are certain routes open to you.

For one, if it's a high school paper, you'd be unlikely to be expected to use primary sources anyway, but even if so, there ought to be some kind of English-language scholarship to draw on, that may have translations of at least some primary material included, either as a block quote or just scattered sentences. How have you been looking for sources? Study of the Bourbon period isn't that limited in English, perhaps if you looked less specifically for Madame de Pompadour, and more generally for the reign of Louis XV, or perhaps even of some gender history on the Bourbon court, you may find more material.

Of course, should that fail, your best recourse would indeed be to find an alternate topic. I'd hope that doesn't happen – it does sound interesting – but if you literally cannot do the project, then you wouldn't be left with much choice. Have you asked your teacher for advice about this? While they may not know the specific topic, they may be able to help with how to move forward.

Absent further information (such as the requirements of this project and time constraints), I don't know how much more I can offer, but I hope this has been a start in terms of some approaches to take, and do feel free to ask further.

Yes, the bottom line is: you need to write about a topic where you have sources you can use. There isn't a way around that one.

But! This doesn't necessarily mean giving up on your topic. Here are some ways to go about it:

(1) Start researching the more general topic and see where the reading/sources take you

You're interested in women's power at early modern/modern courts, and especially the power of courtesans. There is a ton of research on the broader matter of women's political power. A lot of it is on queenship, specifically, but don't be turned off by starting there. You'll find really solid background info there, as well as more specific information that can start to help you develop an idea. Maybe there are other, less well-known women with dramatic or just attractive stories.

(2) Look at what primary sources you DO have

Did Poisson write anything? How about any of her confidantes? She's a popular figure; if she had a letter collection or something, I bet someone in the 19th or early 20th century translated it into English and published it. If so, you could think about how to frame your research topic based on what you get from it, and use other scholarship to contextualize.

(3) Use the primary sources that are cited in your secondary sources

If you don't have access to the actual documents, just grit your teeth and rely on other people's partial use of them. We've all done it.

(4) Keep looking a little longer

Some research tips for finding sources: use the References section on Wikipedia. If it mentions books, read academic book reviews to find out if the book is worthwhile. If the Wiki article on Pompadour misspells one of the linked articles as 'Theatres of Power,' search instead for 'Theaters of Power'. Also look at the general themes--there's a lot of discussion about Pompadour and patronage; maybe some scholars have placed that in the framework of political power?

Hopefully this gives you a few ideas!

There's an extent here to which our opinion is not that relevant here - what matters is what the person marking your essay expects, which we simply can't know (at least, not without you revealing information on the internet that you really shouldn't). When I was in high school, even when writing on non-Anglophone historical topics, it would never even have occurred to me to do research in other languages than English. Even for Anglophone topics, I would not expect that my research was comprehensive in any meaningful sense - some relevant sources would have sufficed, not all (or even a representative selection). Your teacher may be more stringent than mine were...

The broader principle at hand here is one of balancing risk and reward. On one hand, you have a topic you're enthusiastic about, you've done some amount of work already and it's a really interesting topic. If I were marking it, I'd be giving you credit for pursuing the idea despite the challenges, and be grateful to read an interesting essay. On the other hand, you are making your life more difficult, and maybe you could write a better essay if researching it was easier - the marker can give you credit for doing something challenging, but they can't give you credit for an imagined essay that you don't actually manage to write. You need to make this judgement for yourself though - not just because the key ingredient of 'marker expectations' is something we can't speak to, but also because these kind of evaluations are part of the assessment. If you are finding this hard, I'd recommend speaking to your teacher and clarifying whether the essay you think you can write will meet their expectations for the assessment.

In my opinion, this very much depends whether you are a grad student or already pursuing a higher degree. Speaking from my own experience as a soon-to-be PhD student, my personal interest laid with the Eastern Balkans. Now I was and still am unable to speak any regional languages besides intermediate level Turkish, but my thesis supervisor was more than willing to let me write a 50-page grad paper on a subject of my choice. From my master's onwards, I encountered much more resistance from my peers and supervisors when it came to using sources in an unknown language or relying on translations, thus I switched to regions whose languages I am more familiar with.

Since French history and thereby its sources have been widely studied and made available in a lot of languages, I'd say that doesn't have to be the case for you. I would however strongly advise you to speak to your supervisor and double check with them as to what they think about the matter. Since I imagine digitalized sources are widely available on the matter, you might also be able to use translation software (think deepl) to identify paragraphs or works relevant to the topic you chose.

This is a conventional enough topic that there is going to be broad secondary literature in English. If you are only finding french sources you are not looking in the right places.

If your high-school teacher is not able to direct you to sources or help you with this I have two suggestions:

1. Look for course syllabi for relevant university-level courses, many of these are available publicly online.

2. Find an academic or postgrad whose research focus is Louis XV or eighteenth century France and send a concise polite email asking if they can recommend sources (in English) on Madame de pompadour. Many academics are exceedingly gracious about responding to things like this despite their heavy workload (tho the response might not come for a week or two).

I had a similar problem recently whilst researching archeological sites in Italy and not speaking it at all. What really helps if you are using online sources (which I presume you do) is DeepL. The translations are mostly accurate, while you usually have to look up some technical terms. If that is not an option for you (you either have to repaste every 5000 words or buy premium), I'd suggest to search for newer, english research. A good way to do this is search for articles that cite the French ones in question.