Would the average 'Celt' that lived before the Roman Conquest and Germanic migrations have looked very differently in terms of facial features, eye or hair color etc., than contemporary people in Northwestern Europe (France, Belgium)? In what way? For example, there are currently a lot of people with brown eyes and black hair in Northern European countries. Is this largely a result of mixture with Mediterranean populations, or did these features already appear in Celtic populations prior to the mass migrations that happened after the Roman conquest?
Quite a bit as we are starting to find out with consumer genetic testing. There are three big companies selling Genealogy DNA kits for $100-200. Results are compared to reference populations based on indigenous people from different regions. One of the most frequent questions people have shared in r/genealogy and other forums regarding these tests are questions about regions. For example, heavy Scandinavian DNA despite ancestors being from the UK. These are typically explained due to the Viking and Norman conquests. There are other more academic studies taking place on these, I would have to link later. But, as consumer start participating in these low cost DNA tests, we are starting to gain a deeper understanding.
I would also suggest you read topics about haplogroups and you can see over the entire human history how genetic mutations help us understand human migration paths.