If your friend is looking into getting into .net for professional purposes, I would steer them towards C# first. That's likely to be much more useful in the long term. Especially since it can be a stepping stone to other C/C++ like languages.
With F# I would bet that they hit some limitation sooner or later where something that could be easily done in C# will take more work in F#. Which could be fine if they have the time/inclination to rough it. I just would not advise F# as a resume builder.