I am writing a research paper based on Joan of Arc and I am having a hard time finding a good monograph.
Yes.
Oh, you wanted more than that? Yeah, that's reasonable.
So the scholarly literature on Joan is massive, as you might expect with one of the best documented (and most controversial) figures of the later middle ages.
I don't know what level your research paper is at (college, undergraduate, etc), or if you've got a specific focus, so these are my broadest possible suggestions for works on Joan of Arc. I've started with a few monographs, as that's what you requested, but there's a wealth of scholarship available, so I've included a few articles as well, and I'd encourage you to seek out more. If your library has access to it, the Brepolis Medieval Bibliography (which would have shown everything I'm about to suggest) is a good start.
My suggestions:
These are the two best modern editions of the primary sources on Joan. Both contain her 1431 heresy trial, and some excellent discussion to put it in context, both historically and as a source, as medieval inquisitional documents can be tricky if you're not used to them. Taylor's contains more supplimentary material, as well as the translation of the 1455-6 Nullification Trial, which may or may not be of use. Both are excellent works, and you can't go wrong with either.
This one's a bit more pop-history, but it's readable, and very useful as a general overview of Joan's life. It doesn't engage too much with the scholarship (though more than you might expect from a pop history), but Castor is a solid historian, and it's a good read.
DeVries, as a military historian, comes at Joan from this perspective. He's not too interested in her as a religious or political figure, but he examines her military approach and her campaigns in great detail, as well as placing her in the broader military context of the Hundred Years War.
Despite the age, this is probably one of the most useful and interesting books on Joan that's out there. It's a brilliant collection of essays covering multiple aspects of Joan's life and career by some extremely distinguished scholars. If you only get one piece of secondary literature on Joan, make it this one.
Warner is a excellent scholar, and this is a good piece of work. It was written at the height of the women's history turn, which means that it's focus is pretty strongly on gender issues, and it's not hugely subtle about it's feminist angle. This is by no means a bad thing, and it's a very productive lens to view Joan through, but newer scholarship has been a bit more guarded about the extent to which we can view Joan as representative of women's agency or as pro-female in the context of the later middle ages.
Focused on the contemporary literary and theological debate about Joan. Really interesting to consider just how controversial she was even amongst the French in her lifetime, and sets her brilliantly amongst the landscape of visionaries, prophecies and discernment of spirits that was raging in the 14th and 15th centuries. Possibly best read in conjunction with the Elliot below.
Some broader suggestions, expanding out from the focus on Joan a little. Some of these will be useless, depends on your angle and area of interest:
If you've got any follow-ups, or have anything more specific you want pointing to, just let me know - if it's not suitable for an extended discussion on AH, you're welcome to drop me a message.