Translation:There is a village by the river.
It can depend on context. In English, when something — usually large and not-so-mobile — is located right next to the water, we often say it is "on" it. It's very common to hear of a city on the river for example, and of course, it isn't actually on top of it.
川のそば is "river's side" (though not quite "riverside") so it is suggesting a very close proximity. "On" would be perfectly natural to say here.
Well, I'm from the U.S and I've probably heard "on" used more for things like cities or attractions, but the way things are said can vary greatly throughout the nation.
For what it's worth, Google's n-gram viewer generally shows "city/town/village on the river" as being more common in either English to varying degrees. Playing around with the type of water and establishment shows some interesting trends, but "on" seems to generally be dominant, though the margin is not currently huge.