Sorry for my English but I am French.
I don't know if your question regarding the piece of steel you have found in Normandy is still active, but I am sure at 99% it is a part of the roof of a Stugeshutz III auf G.
This piece is the half of the roof around the target sight. On the Stug III auf G the sight was going through the roof as an episcope or a periscope.
So it is German relic but not from a Tiger, not enough thick. The tiger roof or hatches were from 20mm to 40mm.