Getting an error when I try to assign a char array via the constructor

You can't assign/copy an array like that in c++. Instead, you could use std::copy to do a copy of the array, in the constructor:

C(char f[255])
{
  std::copy(f, f + 255, field);
}

I suggest using std::string instead of char[255]. Then your class simply becomes:

class C
{
  std::string field;
 public:
  C(std::string field) : field(std::move(field)) {}
};

This way you don't have to worry about the array being large enough.

You can't copy an C array with the assignment operator but C++ provides std::array:

class C
{
    std::array<char, 255> field;

public:
    C(const std::array<char, 255> &field) : field(field) {}
};

If you can use dynamic memory allocation and the size of the field can also be dynamic you should prefer std::string:

class C
{
    std::string field;

public:
    C(const std::string &field) : field(field) {}
};

In a function parameter, a char[] (with or without a number specified) is just syntax sugar for a char* pointer. And you can't initialize a char[] array with a char* pointer, hence the compiler error.

For what you are attempting, you must copy the memory that the char* is pointing at, eg:

class C
{
    char field[255];

public:
    C(char field[255]) // aka C(char *field)
    {
        memcpy(this->field, field, 255);
        // or: std::copy(field, field+255, this->field);
        // or: std::copy_n(field, 255, this->field);
    }
};

Alternatively, if you want to ensure the caller can only pass in a char[255], pass it by reference instead of by pointer:

class C
{
    char field[255];

public:
    C(const char (&field)[255])
    {
        memcpy(this->field, field, 255);
        // or: std::copy(field, field+255, this->field);
        // or: std::copy_n(field, 255, this->field);
    }
};

That being said, you should consider using std::array instead, then you can use operator= assignment like you want:

#include <array>

using Char255Array = std::array<char, 255>;

class C
{
    Char255Array field;

public:
    C(const Char255Array &field)
    {
        this->field = field;
    }
};

Or better, use the constructor's member initialization list:

#include <array>

using Char255Array = std::array<char, 255>;

class C
{
    Char255Array field;

public:
    C(const Char255Array &field)
        : field(field)
    {
    }
};

Raw arrays are not recommended to use in c++, you can read about vectors and arrays classes they are more usefull. Although the solution for your problem is you just need to change the type of the attribute field to char*, and it works perfectly. for more explanation: in c++, you can assign to a char* type a char array but the reverse is impossible because the pointer is only pointing on the first character.

class C
{
    char* field;

public:
    C(char field[255])
    {
        this->field=field;
    }
};