Just wrap a structure around it?

struct Char32 {
  char data[32];
};

void func(Char32 &param) { ... };

I would recommend using std::array to avoid all the messiness with decay to pointer. std::array is not like std::string, because it is a fixed size array that does not dynamically allocate memory.

As for std::array being owning, there are proposals to add array_view to the standard, which is a non owning range. This has the primary benefit of allowing the various ways that a sequence of objects are represented in c++ to converted to the same interface. But if you don't need a vector of 32 elements to be acceptable input then a reference to std::array<char, 32> is sufficient.

The syntax for array passing is crazy in C++ but this will do allow you to do this:

template <size_t charCount>
void stringCopy(char (&output)[charCount], const char* source)
{
}

I highly recommend you use a template on the array parameter here because this function now works with any sized arrays.

In this case the size is known, so you don't need the template:

void stringCopy(char (&output)[32], const char* source)
{
}

But I still recommend using std::array.