Actually, No.
There should be a server git repository and local git repository. For local git repository , you just need to make sure the user have windows folder permission. However, for server git repository, which is also host on TFS server. To access server side GIT repository, you also need TFS access.
To license TFS , you’ll need a TFS server license and a Windows
operating system license (Windows Server is best) for each machine
running TFS, plus a client access license for each person connecting
to TFS. Client access licenses (CALs) aren’t required for people who
just access work items – assign them “Stakeholder” access, which is
free.
Only the Stakeholder access is free and no need a CAL. GIT repository access
is also belong to Code feature which at least need Basic access

More details about access levels please refer this tutorial in MSDN.