I'm very interested in pursuing a personal research project concerning French troops in America during the American Revolution. I've been attempting to locate where original manuscripts by some of these soldiers might be, but I don't really know how. I've run into this problem of finding primary source documents many times throughout my research. Are there any specific websites, certain archives, or general pieces of advice that can help me? Thank you very much in advance!
One of the first steps in any project is usually reading what has been written about the Revolutionary War or specifically about the French involvement. Aside from giving you an idea what has been written, this can be a key step in finding out where material might be. Always check the citations and bibliography at the back of a book (assuming it’s an academic one). This can be a great way of just getting an idea where stuff is, do this enough times and you can get an idea of where things are concentrated and where the richest collections might be housed.
Often times that’s the best place to start, once you know the given library, archive, or institution where things are, they may have finding aids, or archival inventories (sometimes very detailed ones), or, there may even be annotated bibliographies for a given archive or collection that you can use to figure out what else might be there.
Finally contact the institution and arrange a visit. Typically most the information you need can be found online for larger and/or government archives, but it’s always good to at least email before and make sure you can visit on a particular day, week, or month. Especially if you are consulting private documents that might require additional approval— or to find out if the documents you want to see are even available. I’ve found often enough to when viewing ship logs for pre-1800 voyages, the originals are not accessible without special permission, rather only copies are available, sometimes which can be copied and sent to you (fees can vary wildly regarding this), thus saving you an expensive trip if there was only one thing you had identified as being of interest.
Additionally, if you go to an archive, talk to the archivists, or the Room Director/President, whoever is running the archives or reading room at the time. Chances are, if they have a lot of material relating to your topic, they may have someone who knows the material well or even specializes in it and can help you find more. Even if they aren’t a specialist in the area they are often more intimately aware of archival holdings not listed on finding aids, or specific ways to search the archive which aren’t readily apparent due to the vagaries of how things are catalogued.
Since /u/b1uepenguin gave you such a nice run-down of the theory and method of archival research, I'm just going to throw you Worldcat with some tips. Many (but not all) major archival papers are going to show up in Worldcat, marked as "Archival materials." The main trick is finding the right subject heading, and hoping the archives cataloged well. Here is a custom search for you under the subject heading United States - History - Revolution, 1775-1783 -Participation, French and limited to archival material (tickies on the right side.) I'm too ignorant of the subject to know if this is what you're looking for, but thumb through it. You can also play with Archivegrid, but I find Worldcat a little easier to use myself. You can also see if you can find any of your soldiers or major people in SNAC, which is an experimental archival discovery tool (works best for people who have wikipedia pages already!)
You might also like this old 2 part post I wrote some time ago on Archives Research 101.