params should always be a dict or a sequence of 2-value tuples, which are then encoded for you. You, however, want to upload an already encoded body, so you want the data keyword instead:

requests.patch(url, data=json.dumps(payload), headers=headers)

In fact, data is the second parameter, so you could even do:

requests.patch(url, json.dumps(payload), headers=headers)

as you normally only send opaque data with PATCH. The .post() and .put() methods behave in the same way, the second parameter is the data keyword.

With pyfakefs, you can map real files into the fake file system. In your case, you can use add_real_file:

def test_json(fs):
    fs.add_real_file("/path/to/repo/test/fake_file.json",
                     target_path="/path/to/file.json")
    assert os.path.exists("/path/to/file.json")

This will map your existing file into target_path in the fake file system (if target_path is not given, it will map it to the same location as the source file). It does not matter if there is a real file at the same location, as the real file system will be ignored in the fake file system. If you read "/path/to/file.json" in your test code, it will actually read "/path/to/repo/test/fake_file.json" (mapped files are only read on demand).

Note that by default the file is mapped read only, so if you want to change it in your tested code, you have to set read_only=False in the mapping call. This will make the file in the fake file system writable, though writing to it will not touch the file in the real file system, of course.

Disclaimer:
I'm a contributor to pyfakefs.