The way that rust attempts to prevent this class of error is not by making an implementation of free that is safe to call twice, but by making the compiler refuse to compile programs where free could be called twice on a pointer.
Anyway, use after free doesn’t depend on a double free. It just means that the program frees memory but keeps the pointer (which now points at memory that could contain unrelated data at some future point in time) and if someone trying to exploit the program finds a way to induce the program to read or write to that memory they may be able to access data they are not expected to, or write data to be used by a different part of the program that they shouldn’t be able to