There is also a possibility that some of the Norman nobility may have worn lamellar at Hastings. Consequently it is recommended that the following restrictions be placed upon the wearing of Lamellar.
The facts are that the Normans were in Sicily before they invaded England, and Sicilian art appears to show lamellar in use. The Bayeaux tapestry has two depictions, one of Bishop Odo and another which could also be Odo, showing a two-toned brown garment worn over mail. This has been postulated to be lamellar, jazerant, gambeson, or simply a rich fabric. So, no hard proof that it was used, but a hinted possibility that it might have been.
ferrum ferro acuitur et homo exacuit faciem amici sui
If I was looking to find some evidence of lamellar use by the "French" Normans, I'd try to find biographical information about individuals who were at Hastings and see where they had traveled. If you find that someone who had campaigned in Sicily, for instance, then it's possible he owned such armour. Armour was expensive, and someone who had bought/stolen/pillaged some nice lamellar would likely have kept and used it, particularly if he liked it a lot.
We also, on the other hand, have significant evidence of mail-wearing warriors encountering lamellar on a regular basis during the crusades, and rejecting it in favor of mail, which provides better coverage and MUCH better mobility, albeit less impact and arrow resistance (for given penetrator/armor matchups at least).
(As a complement on top of mail, East-Euro style, it's a possibility... but we're talking, imho, a pretty serious outlier from the norm)
No one cares how much you know, until they know how much you care.