How to cast float into four bytes?
You are getting exactly what you said you want. 4 bytes representing the number in float format.

What you are expecting to get, is 4 bytes representing the number in big-endian integer format.

Using Majenkos solution for casting, you need to change the types and reverse the for loop for big-endinaness.
I also used int32_t because the size of the int is 16-bit (2-byte) on the Arduino Uno (and other ATMega based boards) and on the Arduino Due it's 32-bit (4-byte). Its better to define the exact int in this case.

union {
    int32_t ival;
    byte bval[4];
} int32AsBytes;

void writeInt32(unsigned int addr, int32_t x)
{
    int32AsBytes.ival = x;
    for(int i = 3; i &gt;= 0; i--) // reverse for big-endian
    {
        i2c_eeprom_write_byte(0x57, addr, myFloat.bytes[i]); // Write byte to EEPROM
        Serial.println(int32AsBytes.bval[i], BIN);  // Debug line
    }
}