Now, while the French would have adapted and accepted new ideas, one has to keep in mind, the German war machine was open to new ideas for a longer time, thus, the two would be in a nearly similar situation.

It would remain to be seen whether France would be able to make up the lost ground, considering that, if Germany was on the winning side (and the US on the losing one), they would be saddled with extreme amounts of reparations, not to mention damage and losses from the Great War. Keep in mind, the US was the one who kept the reparations smaller, the European way was always: Vae Victis. France would not be able to recover soon.

Britain would probably get involved, if they thought they could win, however, following a defeat in WWI due to Naval power of Germany, the Royal Navy would have been limited and weakened in the aftermath, not to mention the loss of colonies which would probably happen with that. Germany, with the massive increase in colonial holding, and the victory through the Navy, would probably vastly increase their own naval power. It would be a close battle for control of the sea.

The US, having been forced to sign a peace treaty, would probably become increasingly isolationist, and wouldn't get involved in such a conflict. On the other hand, it might shift to more extremist positions, but in that case, it would mostly keep itself centred on the Americas.

Italy itself was fairly fragile, and it's fate following WWI would be uncertain. Keep in mind, despite the victory, Italy was unstable, leading to the rise of Fascism, Italy was only united for a brief time ... and the defeat might even have caused it's collapse, akin to that of the Austro-Hungarian Empire, which, probably, would have survived, albeit greatly weakened and in a different, more diffuse form.

Russia would keep out of any such war, and considering that Germany would probably interevene in the Civil War in support of the Whites, they might even favour the Germans, thus adding the vast resources of Russia to their war effort.

Thus, as I see it, a second war would have, in this series of events in a German victory and a second defeat of France and Britain. Something, I believe would have led to the collapse of both countries.