Specification

Replace the contents of the string.

Signature

UTF8string& utf8_assign( const char * str )
UTF8string& utf8_assign( const u8string& str )
UTF8string& utf8_assign( const u8string& str, size_t pos, size_t count = npos )
UTF8string& utf8_assign( UTF8string&& u8str )

The problem

UTF8string internally uses std::string. However, std::string is an alias of std::basic_string<char>.

This is a problem because each byte of UTF-8 characters are encoded as an "unsigned char" between 0 and 255 (0xFF). So, when I check if a string is utf8-valid, I check it as an std::string (sequence of char) instead of as a sequence of unsigned char ("real bytes"). Consequently, I have some troubles with byte comparison (unwanted implicit conversions (>.<)).

Possible solution

I think it should be very helpful to use an std::basic_string<unsigned char> instead of std::string in order to handle the internal string properly. Fortunately, the interface does not need to be changed.

The way you validate 4-bytes utf8 character is questionable.
The first of 4-bytes char must be between 0xf0 and 0xf4, which you forget to test.

            // If the first byte of the sequence is 0xF0
            // then the first continuation byte must be between 0x90 and 0xBF
            // otherwise, if the byte is 0xF4
            // then the first continuation byte must be between 0x80 and 0x8F
            if(*it == '\xF0')
            {
                if(*(it + 1) < '\x90' || *(it + 1) > '\xBF')
                    return false;
            }
            else if(*it == '\xF4')
            {
                if(*(it + 1) > '\x8F')
                    return false;
            }