A fairly good short account of the capture and early occupation of Berchtesgaden was written up here by John McManus, a well regarded military historian.

The relevant quote is:

Thus, as the war ended and the 101st Airborne Division occupied Berchtesgaden and its environs, the mistaken notion that they had bagged this great prize took hold. Thousands of tourists from the Allied armies visited Berchtesgaden that summer. Since the paratroopers were there, most of the visitors assumed that they had taken the place. The Screaming Eagles had the time and opportunity to pick the town clean of prime souvenirs...

Which means to me, that the helmet could basically belong to anyone, since the area was visited by numerous units during the occupation and could well belong to any unit using a U.S. pattern helmet which included many French units known to be in the area.

That is a Belgian, or other non-US manufactured pot, post-WWII manufacture, and that silica texturing dates the paint to late 1960s at the earliest. Steel rim with no front seam is a dead giveaway, however.

Edit: upon further inspection I can't conclusively say whether or not there is in fact a seam on the front of the rim. Its presence or absence would almost certainly verify all of this.

Edit 2: Can't say I'm even 100% convinced that isn't cork texturing based on the one picture. If I knew what kind of bales it had on the sides and where the seam on the rim met I could give you a more accurate idea of what exactly you have there