Editing software to quickly match audio and video transitions
From a quick Google search, I can see that Movavi has something like this and (as far as I can tell) is free. However, it only marks the beats for you; you'd still need to actually roll up your sleeves and cut the clips down yourself.

Adobe Premiere Elements also has a beat detector thing (I believe) but, again, I suspect that it'll just help by marking the beats on your timeline, leaving you to do the cutting.

I can't actually find something that does it all for you but, to be honest, you'll probably get better results cutting the thing yourself and it really won't take that long (I reckon about an hour or so for a 2-3 min track, if that - especially if you've already selected your clips).