Well, there's two different contexts in which to take this question. Most D&D games don't really run authentic late Middle Ages, they run a cleaned up, idealized, 20th century infused view of it, where families live in nice little cottages and there's glass in all the windows and there aren't kids dying of disease and starvation all over the place and the like. But it's not just lower standard of living; also a lot of the real science, banking, law, and such that was emerging in the late Middle Ages tends to be ignored for simplicity in games. Real late Middle Ages would be as shocking to the average Forgotten Realms player as any other age, mainly because of the profoundly different mindset of cause and effect they held.
So is the question "how is Clean Fantasy Iron Age different from Clean Fantasy Medieval?" The answer to that is generally just the armor/weapons and local color like painting faces blue and more hillforts less castles.
Or is it "how is Authentic Iron Age different from Authentic Medieval?" That's an interesting question, and they are very different in some ways but similar in others. The Hallstatt and La Tene Iron Age cultures (two different eras for the Gauls within the 800-200 BC range you cite) were increasingly influenced by the Greeks and traded for luxury goods from the Mediterranean and, through fundamentally tribal in nature, also had larger scale government in place and surprising political complexity as explored by Caesar in his commentary on the Gallic wars. Romans came, Romans went, and over the course of the Middle Ages "tribal but influenced by the Romans" wasn't that different from the Iron Age. In fact, the larger political divisions were coopted by the Romans for rule and later by the Church for ecclesiastical boundaries.
The ubiquity of Christianity (usually absent in Clean Fantasy Medieval of course) is the single biggest change from the animistic and less theological worship of the Gauls - though note if you're running "D&D worlds" they tend to be polytheistic and whatnot anyway, so there will be much less differentiation along this axis. Also, the learned "druid" class was in charge in Iron Age Gaul, which in practice is pretty similar to having the Catholic ecclesiarchy in charge. There is more sacrifice (including human) and belief in "superstitious" signs and omens (though again, this was in actuality just as common in medieval times, though unusual to us moderns).
There's not as much construction (large ruins, constructed dungeons, 300' towers, etc. will be largely absent) and cities are smaller, life is more rural and agriculture less developed, so less "farms and big castle" and more "village with hillfort and hunt/gather/small farms spread out around it." Literacy is less widespread than late medieval/D&D (though about equal to real Early Middle Ages).
Combat is frequent though usually tribal in scale so swords are common; real Celtic combat was Greek influenced and used phalanxes, chariots, and bows.
So the short list of things one would see at first glance:
- Politics: Tribe is super important and is the core part of people's identity
- Religion: Pagan animism/polytheism with sacrifices (including human) common; druidical class is on top politically as well; superstition and fairy folk stuff is big
- Artifacts: Less developed architecture and missing higher tech armor/weapons
- Practices: Head-taking in combat. Tribal warfare common but generally small in scale