Why does there need to be a WW1? It's evidently butterflied away...
Mhh i rechecked the map and you are right, it's evidently 1920. Maybe the mentioned Franco-Prussian war is this TLs WW1 (i assumed it was similar to OTL).
I just thought with no major change in Europe (besides France never selling Louisiana - btw did they lose it to revolution like Great Britain losing the US?), there might be war looming. And as Iserlohn stated, there is probably bound to be one (weapon's race in Europe, nationalism and such), until such a thing like European Unity comes around when there comes the Red Threat (assuming Russia is just as fucked in this TL (maybe not as much, since there is Russian Alaska still) and commies take over).
As i said, this could be a very interesting world.