This apparent error is actually an interesting subject that has received some attention recently, years after your post. The Wikipedia article claims that the gun in question may have been a .45-70 Winchester underlever rifle or a .30-06 Winchester M70, but in his own words, Fraser was carrying a light, short-barrelled US army carbine and I don't see any reason to doubt the man.
In my opinion it's not entirely unreasonable that Fraser could have a Garand. Given his position as a Brigadier (general) and CO of a commando unit taking part in D-Day, he could have just popped down to the American camp and said "Righto yanks, toss me a rooty tooty if you please. Cheers big ears and bob's your uncle".
It could also be a Lend-Lease rifle and the artist missed a crucial detail: Britain didreceive some M1s as part of the Lend-Lease program, but these had a red band of paint on the handguard with the caliber stenciled in black.