Communication between Genuino Zero and Arduino Uno using UART
Your Arduino Zero transmitter code transmits to the USB Serial ('Serial') only. If you want it to transmit to the serial comm on pin 0 and pin 1, you must have it write to Serial1. (Check variants.cpp file ) you will see that Serial1 is uses SERCOM0 which is on pin 0 and 1.

So, Your code should look like this (noitce "Serial" is replaced with "Serial1"):

void setup() {
  // initialize serial communication at 9600 bits per second:
  Serial1.begin(9600);
  // make the pushbutton's pin an input:
  pinMode(pushButton, INPUT);
}

// the loop routine runs over and over again forever:
void loop() {
  // read the input pin:
  int buttonState = digitalRead(pushButton);
  // print out the state of the button:
  Serial1.println("a");
  delay(1000);
  // delay in between reads for stability
}