Assuming Maximilian is kept in power by the French, how does a Mexican Empire under a French puppet effect everything?
Would France seek to undermine the United States in hopes of strengthening its hold on Mexico?
What if Mexico could industrialize, and Maximilian and his descendants slowly turn strong, forging a hard line, first world state out of the country.
When the Great War breaks out, the Mexican Empire, France, Austria, and Spain fight the Germans, Russians, and Italians over the assassination of German crown prince by an Austrian terrorist. The first shots of the war are fired in 1912, with German forces managing to hold off a combined Franco-Austrian offensive.
As the war goes on the Germans and Russians manage to overpower the Austrians, forcing the Treaty of Belgrade, in which Austria is forced to grant Hungary and several other ethnic groups independence, leading to a reduced Hapsburg state owning Tirol and parts of Croatia, Bohemia, and Slovenia.
The military attempts a coup, but it is mercilessly put down. With Austria fallen, the Imperial Alliance (Germany, Russia, and Italy), turn on France, with Italian and German forces forcing through the French lines, breaking them and driving for Orleans and Paris respectively.
After the initial successes the French manage to stem the line with the arrival of Mexican and Spanish forces, reversing it with a counter offensive in mid summer of 1915, driving the Italians out of the country.
A second front is opened in August, with the Mexican and Spanish navies coordinating and opening a Front in Sicily. With the invasion of Italy the Italians pull back most forces from the French front and focus on the south, leaving the north with a skeleton force.
At this time, the Ottomans see an opening to exact revenge on the Italians for the loss of Libya, and in the days following the invasion of Sicily, the Ottoman Empire declares war, landing soldiers in Libya and the Italian Mediterranean Islands. While not officially allied with the French Alliance, the Ottomans are co belligerents.
The Ottomans opening of a third front leads to an internal power struggle in Rome, with the government managing to reassert control, but only after the northern front collapses, leading to the pouring in of Allied forces. By the time they reach Milan in 1916, the Italians call for a ceasefire, with about half of their country under occupation and their colonies falling to the Ottoman onslaught.
The terms for peace do not come cheap to Italy, they are forced to cede Libya to the Ottomans as well as the minor islands of the Mediterranean Sea. The Ottomans, French, Mexicans, and Spanish all take part in the Rome Conference. The Ottomans officially join the Allies, with the Italians losing large chunks of the north to the French, and a Sicilian occupation zone is set up in order to demilitarize the region to prevent any blocking of Allied vessels and to make sure they have refueling stations. All other African colonies are transferred to France.
With the fall of Italy, the Allies have unrestricted access to the Mediterranean Sea. While the German front is more stable, the Russian-Turkish front has become a sloshfest, with the front lines moving back and forth over the course of the war.
The war drags on for several years until 1921, with the two sides failing to gain an edge over the other. A conference is called in Brussels as the terms for a ceasefire, which goes through on January 16th. The treaty of Brussels restores pre-war borders between Germany and France, while Russia loses some minor territory in the Caucuses to the Ottomans. The Treaties of Rome and Belgrade are to be respected by both sides, and peace is declared on March 13th.