A riff on @AndyD273's answer:
Pitchblende was only known in the middle ages from one place in what's now the Czech Republic. But 1% uranium Oxide yellow glass was found in Ancient Rome over 2000 years ago.
Isolating Uranium from the ore is not simple.
Some organisms can concentrate Uranium. Citrobacker can encrust themselves with uranyl phosphate crystals. Some lichens concentrate uranium, and some fungi cause plants to concentrate uranium.
Precipitating the metal involves extreme alkali solutions, which makes me think of dye making. What if… wode dye craftsmen found another plant (or lichen) that produced a vivid yellow dye, and cultivated a source of uranyl phosphate. Their use of extreme alkali solutions, and skill transfer with those also working with lye and nitrates for gunpowder manufacture leads to purposeful experimentation and careful note taking of anything odd, because of lucrative history in that area.
So they stumble onto "dark gold", which is noticed as being as heavy as gold; heavier than lead and like nothing else except gold. Given the association with yellow colored dye, alchemists jump on it thinking they are close to making actual gold.
The next problem is in recognizing what it can do. Before photography or real chemistry, how could they tell that Uranium was doing something?
Fluorescence was reported as far back as 1560. Many fluorescent materials exist in minerals and organics, and without a source of UV light nobody noticed the effect. Some fluorescent material, or a mixture of florescent emitter and a UV emitter, might give off visible light when subjected to ionizing radiation.
What if dyers used Umbrelliferon as a cloth whitener? Now that process uses alchohol not alkali, but treated cloth might glow in the dark when exposed to the dark gold.
The underlying problem is that Uranium isn’t that spectacular without making an atomic pile or having some atomic theory that was discovered because of radioactivity. The build up of daughter elements makes it more radioactive and toxic as it ages. Once radioactivity is “seen” through fluorescence, the quest might be undertaken to isolate the radioactive part, and harvest what seems to be produced over time. Without chemistry, that seems like a haphazard endeavor. But in our fictional world, practical pre-chemistry might be more advanced as an art, with the rich dye-makers’ history and now culture of experimentation.
This alternate history of early discovery of radioactivity doesn’t end up with practical weapons though. Although I like Heinlein’s idea of using toxic radioactive dust (written when it was thought that a chain reaction was not possible), a toxic radioactive powder would be very expensive and impractical for this pre-technical society to use as a weapon.
The same industry, on the other hand, would have produced explosives a lot better than gunpowder, and nitrates would be weaponized, rather than radium. Radio-isotopes would be used for instruments and maps that can be read below decks, but not bombs.
footnote: For more on wode dye and alkali solutions, see Tony Robbins Worst Jobs in History. I suppose it would be the Anglo-Saxon episode. You might find it on Youtube.