Why didn't he shot/wound any of the attackers?
I cannot think of one reason why he moved to france, some said as the reason why:
Peiper chose France because he loved the scenery, and a man whose life he saved offered him a piece of land.
I had heard that he moved to France where he could be someone who would be "lost" to the world and that he could live in relative obscurity
Why didn't he shoot his attackers?
A weapon (Normally: .22 Kal) has been found next to him after they found him after he was burned to death.
It was an "evidence" of a struggle/fight with (one of) his attackers..