GHPythonRemote only works in Python 2. You need to create a new Python 2 environment in order to install it.
A python virtual environment is basically just a folder where one python.exe executable is kept, along with its standard library and any user-installed packages. All the versions of these have to be compatible with each other, in particular it is not possible to have two different python.exe in the same environment.
The best way to install GHPythonRemote for you is to create a new virtual environment in Conda, based on the latest python 2.7. This procedure is explained in the documentation. You will need to install all the other packages you need for your scripts in that env.
If you are looking to use CPython in Rhino and can access the latest WIP version (Rhino 8), I highly recommend you check out the new script editor. It has built-in support for CPython in Rhino.