I'm currently working with a team on a software project at school. I am the only one contributing to one of the folders that contains all C++ files. I already have my personal GitHub link up on my resume, but I would like potential employers to see the work I've done on my team project as well as it is pretty significant. When I list the project on my resume, should I include a link to the folder in my team's GitHub organization repo? Should I fork the repo and only keep the files I've worked on? Not sure how to go about it.
You can link to anything that's public-facing and there's nothing wrong with letting people know which public-facing projects you've been contributing to as long as you don't claim to have done more than you did.
From the github privacy statement:
Much of GitHub is public-facing. If your content is public-facing, third parties may access and use it in compliance with our Terms of Service. We do not sell that content; it is yours. However, we do allow third parties, such as research organizations or archives, to compile public-facing GitHub information
Ideally you should be using your own account to identify which changes truly were made by you, for the sake of the company and yours, but if you're using a team account of some sort make sure to give a brief description on which part of the project you participated in.
Forking the repo for the sole sake of keeping individual files is probably not such a good idea since the files might appear as out of context. Simply referring to the original repo and identifying which section of the project you handled all by yourself should be sufficient. You might want to own a backup of those or have access to previews versions if major changes are made and you want to be able to show the original files later. You should absolutely never do this for private-facing projects since they are 100% owned for edit and view by your company.