You should try to test only what your user would see in a real browser, and not your component internal logic. This is what react-testing-library promotes : writing tests that give confidence because they see/do what a real user would.
https://testing-library.com/docs/guiding-principles
Following these guidelines, you should try to build a test which triggers user interactions on visible elements (rendered by your component), and which would involve the execution of simpleMethod.
This is the whole point of react-testing-library queries : getByText, getByPlaceholder, getByRole : things that a real user would see, hiding internal logic. But I guess you could have this approach with Enzyme (I never used Enzyme).
Writing tests with this approach leads to less tests, but stronger ones, which IMHO is a good thing. It is quite different from classical unit tests (say in a Java context for example) where you tests functions, inputs, outputs...
In fact your React component is a function, its inputs are user interactions, its output is a DOM.
simpleMethod?