They might stick with bows and crossbows a lot longer
Black powder weapon advantages
There are basically two advantages to early gunpowder-based weapons, that both turned out to be quite useful in early modern Europe, and led to further development:
Early modern Europe had mostly small armies, and lots of castles with tall but relatively thin walls that were easy to defend with small garrisons. These are almost uniquely vulnerable to early cannon. It took some time to develop cannon to the point where they could rapidly and reliably batter down those walls, but once that was achieved, walls suddenly turned out to be almost useless. (this didn't apply in china, as they mostly used much thicker walls, filled with earth)
This led to the development of fortifications with thicker, lower walls, but those couldn't rely on the difficulty of scaling them, so you instead needed a large garrison that could effectively threaten attackers. That leads us to the second advantage:
Guns are easy (relatively speaking)
That's not to say that a gun is trivial to make, to make ammunition for, or to operate, but it is much faster and easier to train a peasant to use a gun than it is to train him to use a (war)bow. So if you suddenly find yourself in a situation where you need to massively expand your army, and arm them with ranged weapons (spears are cheap and easy, but they won't help you much when defending a star fort), in order to defend your fortifications, they're the best option you have. This was very much the case in early modern Europe.
So what happens without black powder?
Well, if the industrial revolution happens, as Ilmari Karonen says, eventually nitric acid will lead to the development of guncotton and other suitable explosives. That will almost inevitably lead to guns. Earlier, the development of pressure vessels might give you airguns, but until either of those are compelling enough to force a switch, armies might continue to use and further refine bows and crossbows.
Gunpowder-based warfare was very important to the political history of Europe. Without it, the nation-states that you know might not exist, which all sorts of knock-on effects.
The industrial revolution
For instance, the industrial revolution might not have happened there, or at all. In Britain, it required large coal deposits, the depletion of forests (for firewood and charcoal), the existing knowledge of early pressure vessels (from black powder weapons), all contained in a large state doing lots of trade (so greatly increasing production of, well, anything, wouldn't crater prices), allowing early "burn coal to power a very inefficient pump to drain the coal mine so you can dig up more coal" engines to be developed and adapted to power factories.