I'd say that it's best to test the API that your users will be exposed to. Other tests are good to have as well, but that's the most important aspect.
If your users are going to write C/C++ code linking to your library, then it would be good to have tests making use of your library the same way.
If you are going to ship a Python wrapper (why not?) then you should have Python tests.
Of course, there is a convenience aspect to this, as well. It may be easier to write tests in Python, and you might have time constraints that make it more appealing, etc.
I guess what I'm saying is: There's nothing inherently wrong with tests being in a different language from the code under test (that's totally normal for testing a REST API, for instance), but make sure you have tests for the public-facing API at a minimum.
Aside, on terminology:
I don't think the types of tests you are describing are "unit tests" in the usual sense of the term. Probably "functional test" would be more accurate.
A unit test typically tests a very small component - such as a function call - that might be one piece of larger functionality. Unit tests like these are often "white box" tests, so you can see the inner workings of your code.
Testing something from a user's point-of-view (such as your professor's commandline tests) are "black box" tests, and in these examples are at a more functional level rather than "unit" level.
I'm sure plenty of people may disagree with that, though - it's not a rigidly-defined set of terms.