There is no universal color or art style that would indicate that something is ancient.
Old stuff would look old. There would be decay.
It would be different than what's current.
Now that you have a Medieval-type world with magic, you've narrowed the question and opened up possibilities.
1) Their understanding of magic was different. Some of their old spells still stand, preserving old places. There might still be a building standing, no roof, things growing everywhere inside, but a beautifully maintained fountain.
Example description: Using detect magic, you can see that it's some kind of combined preservation and constant cleaning spell, more complex than anything you've ever seen. There are bits of the magic clinging to parts of the room, and in those places, you see gleaming bright purple tile, crumbling walls standing when they ought to have fallen many hundreds of years ago, next to foliage growing through, and even, a giant oak. The branches shadow the space, replacing the ceiling with sky and greenery. The magic is strongest at the fountain in the center of the room. The fountain looks as though it had been built yesterday, with the bright purple and white tiles and crisp, clear water. --This description uses the setting and the things that have grown there to establish that it's old--oaks take a while to grow, and with the magic slowing the decay, the characters have no real way of knowing how old exactly it is, but it gives the impression of age. Show the decay and use magic liberally as part of the setting. Even if they can't detect magic, the old tree is a great establisher of age.
2) Have the characters discover things that they have no idea what they are used for. They might have all traveled by floating discs at high speed. But the characters don't know that, they just see all these now non-magical discs scattered all around the city. Essentially they were cars/transport. Don't EXPLAIN everything to the characters. Leave an air of mystery. Describe objects that you know what the civilization used them for but that any outsider coming in a hundred years later would not know. Discs are one idea, could be anything. The Egyptian example is the weird perfume cones they used to put atop their heads. If you saw a picture you would have no clue that's what it was unless someone told you. If you found one, it's pretty likely you would not know how it was used.
3) Fashion. Scrolls or wall art might also be magically maintained so that you have pieces of the culture right the heck there and in full color. As to how they dress, if that's depicted--just make it something strange to the current folk. So, like those cone hats from Medieval times, or the super curly-toed shoes--those are pretty dang weird to us, so you have the option of making up some bit of fashion frippery that isn't common to your "modern" folk. Can be anything. Painted nails, chains from the earrings to nose rings, a lack of pants, wearing only pasties, wearing the largest shoulder pads possible, jackets made only of spikes, and so on. Depends on the actual feel of your culture as to what they might do and that's up to you.
4) Colors. So for Egypt, we have something called Egyptian blue. It's the signature color of Egypt, and one of the earliest pigments. Your civilization can have its own signature color or even a combination of colors. It can be any color. Or any combination of colors.
5) Things are lost. For a lot of old cultures that were looked at by Medieval times, they were looked at with a sense of wonder...The Romans weren't that long ago, and yet, they knew how to engineer and do things that people of Medieval times just couldn't do, especially a few hundred years in. The Dark Ages, Medieval times, whatever you want to call them, ARE in fact the inspiration for Tolkien's world, so you can echo that by a sense of wonder at older civilizations--the secret for Greek fire, lost mostly, architecturally the way the Romans built pretty much everything--lost for hundreds of years...My point is, there's the way we in the 21st century look at the Greeks and the Romans, and there's the way the Medieval culture looked back at them, and it was totally different. We've found remnants of gear-driven stuff in Greece, advanced clocks, things of that nature. And they had plumbing in the Roman towns--something that totally went out the window a few hundred years later.
6) New can be old. Ok. Modern day. Imagine an apocalypse. Now imagine that the society builds back up to Tolkien levels, and magic is introduced. What components of our civilization would survive 300 or 1,000 years later? It would be ancient from the perspective of the people. The thing most likely to survive might well be plastic.
7) Legends. I'm not going to give you legends. You have to figure out both the cultural tilt of the current society and what their own lore and modern stories are told vs. how their viewpoint might shape whatever is left of the old society. The old society might have a pantheon, or they might have believed in no god at all, or that there was one god, watching, and it was important to give that god a good show or the god would destroy the world. That's one idea. I am sure you have ideas of your own that are not mine. Greek and Roman myths survived because priests of the Christian religion wrote the pagan myths down. There's no way to know what was lost or gained in these stories.
8) Ask: Is your civilization iconic or mostly unknown? Government, religion, fashion, and morals might not be directly on display in a way that the characters understand. Picture a mural of senators debating from Roman times. Now, what if you didn't know they were debating? What if you didn't know they were senators? What conclusions might you draw? For us in our world, the Roman senate has culturally served as a model for some of our art. We recognize it instantly. So the question is, has any part of the culture become a cultural touchstone for the "modern Tolkien culture"? Or is it totally undiscovered? With no part of its stories and lore passed down, how it's seen will depend on this factor. We know a little something about the Greeks and Romans because of books which were written and copied. We know less about the Aztecs because their stories weren't passed down as much. Mostly, we have to guess. Decide how much and what parts of the old culture has influenced the new, and how much might be open to misinterpretation. Like Regency France was influenced by classical Greek sculpture, so you might see gowns there following some of the same lines. Therefore--put it in one of two categories a) An iconic ancient culture (ie Egypt) or b) A super mysterious culture that's known but hasn't had an appreciable cultural impact on the world (Aztecs). Now an iconic culture can still have plenty of mystery (the Greeks, Romans, and Egyptians certainly do) but they might have bestowed some recognizable ideas and fashion on the world. There are some I consider in between--I think Celtic, in my eyes at least, is a good example of an ancient culture squarely in between the two. Lots of what we think we know of them is largely conjecture, but much of their iconography has had a cultural impact.
