You are being nitpicky about the names while missing the substance. The first battle was the French capture of Saarbrucken. So no, Prussia did not "attacked first".
You are right that behind words like "attack" or "Germany" they are complex human interactions that are hard to understand in retrospect, but I fell obligated to push that discussion a little further: https://en.m.wikipedia.org/wiki/Ems_Dispatch
And because Prussia mobilized much more effectively, it attacked France first.