You are looking at General Order Number 3340, issued under War Department memo 45, which pertains to the four campaigns your grandfather participated in :
Normandy, 6 June 44 / 24 July 44 Northern France, 25 July 44 / 14 Sept 44 Rhineland, 15 Sept 44 / 21 Mar 45 Central Europe, 22 Mar 45 / 11 May 45.
That was a lot of combat in a relatively short time frame, wasn't it ?
The medal you are looking for is the EAME Service Medal.
The four bronze stars attached to the EAME Ribbon represent the four referenced campaigns.
Most GIs would have qualified for the Good Conduct Medal, simply for the fact that they acted as good citizens, if for no other reason. It would have been awarded for stateside as well as for foreign duty.
If you will indicate the date he left the states and the return date, perhaps I can identify the ship/s he sailed on. The dates will be found on his discharge (separation papers). OK ?