How Likely Was a French Alliance with Italy or Japan in World War I?

Short answer: Quite likely. That's demonstrated by the fact that France was actually allied with both Italy and Japan in World War I.

France and Italy made common cause against Austria in the 19th century. France is also a traditional enemy of Germany's, and Italy has few common interests with Germany (Italy defected from the Triple Alliance with Germany and Austria and joined the Allies in World War I.) So a French-Italian alliance is certainly plausible, even in a game.

France and Japan is a little iffier because of the distance between the two countries. But here, they had a common enemy in Germany in World War I, when Japan attacked and took German-occupied Tsingtao (actually a part of China). Japan and France also shared an alliance with Britain, and could therefore have been direct allies as well. In a game scenario, France and Japan might find themselves with "second rank" navies making common cause against Britain's first rank naval power.

It sounds like this is a game others are participating in, so I'd say a lot depends on how the other alliances are shaking out. What you have to look at is what each country wants and what it is (or would be if things work out) in the power of your country to give.

In the case of Japan, what they wanted in 1914 was a bigger role (empire) in east Asia. That means they'd like one or more of the following (in rough order of Japan's 1914 priorities):

1. A free hand in Manchuria/China
2. Russian Siberan territory
3. Some of the European/American possessions in SE asia.

Number 1 frankly anybody could offer. However, Russia had interest in the same area.

Number 2 implies both would have to be at war with Russia.

France could certianly offer some of Number 3, no matter how the alliances end up shaking out. However, their opponents could as well (particularly French Indochina). Also, #3 would be quite difficult for Japan to pull off if the British navy was opposed to the idea (which is why Japan and England had a naval alliance at the time). So to make #3 viable, France and Japan would probably have to be also allied with England, and going up against Germany and the Netherlands or against the USA (Phillipines).

So most likely an alliance with Japan would require (and be most useful) in a situation where Russia is on the other side. In a pinch, you could convince them to go for the southern expansion option, but in that case it would only be feasible if Germany and the Netherlands are on the other side, or the USA is on the other side.

I recommend that you do some research into World War I, at least read this Wikipedia article on the subject (note: the section marked "belligerents").

More important than knowing who was who's ally, you need to know why the war started in the first place. Knowing that will give you an understanding of why major powers acted as they did. From the wikipedia article outlined above,

Long-term causes of the war included the imperialistic foreign policies of the great powers of Europe, including the German Empire, the Austro-Hungarian Empire, the Ottoman Empire, the Russian Empire, the British Empire, the French Republic, and Italy. The assassination on 28 June 1914 of Archduke Franz Ferdinand of Austria, the heir to the throne of Austria-Hungary, by a Yugoslav nationalist in Sarajevo, Bosnia and Herzegovina was the proximate trigger of the war. It resulted in a Habsburg ultimatum against the Kingdom of Serbia. Several alliances formed over the previous decades were invoked, so within weeks the major powers were at war; via their colonies, the conflict soon spread around the world.

There were two major foreign policy trends in Europe at the end of the nineteenth century; colonialism and ensuring the balance of powers on the European continent. The major powers of Europe (Great Britain, France, Germany, Russia, Italy, Austria-Hungary) were motivated by the memory of the chaos caused by Napoleon's conquests in the beginning of the century and the instability caused by Prussian conquest (Prussia was the per-cursor to Germany, the latter formed at the end of the Franco-Prussian war in 1871). They built a network of alliances to ensure that no European country would dare to go to war in Europe for fear of having to face not only one country, but all of that county's allies as well. The two allied blocks managed to keep Europe peaceful for almost a century managing a balance of power until the events mentioned above.

While Europe remained of limits to expansion for those major powers, much of the world was open for exploitation. Much of the conflict between European nations was restricted to competing over territories in Africa, Asia, and the Americas instead of fighting for the more difficult to acquire land and resources of Europe. Thus, when the massive network of alliances failed to prevent a European war, not only was the war fought in Europe, but amongst the colonies of the major European powers as well. This is why World War I is considered by many to be the first truly international war.

Look into the major powers above, for more on Italy read this. Look up the "Triple Entente" and the "Triple Alliance". Those were the two major blocks of alliances which were supposed to keep a European war from happening.

Also, on the role of the United States and Japan. The US spent most of the war trying to stay out of the European conflict. The US public was not willing to go to war in Europe, and it wasn't until this event that the US started to change their mind on the issue. I would look into that and the German reaction to said event to learn more about whether America would be a potential ally in your re-enactment.

Japan was also cut off from most of the conflict geographically speaking. However, the Japanese used the war much like they would the next world war, as an excuse to expand their territorial holdings at the expense of another major power. Look here for more information.