Since most of the discussion so far has been about history and possible civ pathways, I've collated everything I can find about the Normans in game abilities from the dev panel and recent stream so we can discuss them!
Unique Ability:
Normannitas: +1

movement to embarked units, +5

combat strength to land units next to coast, +30%

production to White Tower
Unique Traditions:
Servitum Debitum: -2

Gold maintenance for Cavalry units
Palisading: +50%

Production to Fortification buildings
Jure: +4

Culture on the Palace, +2

Happiness on City Halls
Familia Regis: +2

Culture for every Tradition slotted in government
Bayeux Tapestry: +4

Culture on settlements not founded by you
Unique Buildings/Improvement
Unknown building 1: Unknown
Unknown building 2: Unknown
Norman Lighthouse: Unknown (ignore this)
or
Unkown improvement: Unknown
Unique Wonder:
White Tower: Unknown
Comments:
- They seem focused on Culture and Military. I wouldn't be surprised if their unique building and wonder were as well.
- They appear to have 5 traditions which is more than the 3-4 of antiquity civs we've seen.
- Keep in mind these are just the traditions that they will keep, we don't know their regular civics afaik
other than one will allow them to build the norman lighthouse.
I have no idea why they get a lighthouse, since I can't find any historical lighthouse this is based on. I suppose its just to help them develop a strong navy (perhaps for future British purposes) and to synergise with their unique ability of being coastal.
Edit: seems that the lighthouse seen in the dev panel is not a unique building.