I've been wanting to depict a cobblestone street damaged by artillery, but how to make it look right? Do cobblestones shatter, bounce upward, get thrown any distances, etc.?

My guess is that it depends on how they are layed:

Typical is packed earth, layer of white sand and then the cobblestones on that, simply in the sandbed. The curbstones are set more stable, often in concrete but between them is a tight packing, nothing more

In modern times coblestone is sometimes laid in a thin layer of concrete. This fixes every stone a lot more.

And finally what type of coblestone. The "all cobles the same" type of "stones roughly the same size"?

I assume the first will get more stoes thrown away from the impact with very few shattering/breaking. Even more so for the "rough" stone variant that has less friction between the stones.

The latter (IIRC a post WWII thing) is IMHO more likely to break stones.

I'm using rectangular stones from Hansa Systems USA and the location is somewhere on the Western Front during World War One, and the cobblestones surround a bronze statue on a plinth.

Well I think the old timey method for laying bricks is more or less the same in Europe with the bricks being laid over an underground of compressed sand. When the underlayer is good the brickwork will be good for a very long time.
My guess is that the bricks in the epicenter will be shattered. Possibly even pulverised. And following the diameter of the blast to the ouside the damage to the bricks should get lesser and lesser to the edge and simply thrown away by the shockwave and the blast throwing up the sand underneath them (hope that last sentence makes... well... sense).

Also depending on how long the crater in your dio exists you can have bricks in the bottom that rolled in after the blast or even due to vibrations of passing traffic.

Hi Tom. Cobblestones are still usead a lot ... especailly in European city centers. As they are set on compacted sand and not fixed, it means they can be lifted easily for pipe and cable work and replaced as easy again, instead of having to lay a whole new surface. Modern cobblestones are quite rectangular with defined edges and corners, but when visiting older parts of cities, the cobblestones are more rounded at the edges and corners.
Of course there could have been newly placed stones as well 1916-1920s, but the rounded edges gives them character and adds to the effect. I have never used the Hansa system, but imagine them to be quite square. Consider this before deciding what method you will use. Personally I think laying a layers of spackel and hand scribing them takes some beating for making natural cobblestones.