Trans-Hemisperic European Monarchy.
POD 1850 - All of Europe is gradually brought under the control of a resurgent French Royal Family; with only the UK, Iceland, & the Danish possession of Greenland still Independent.
THEM attempted to intervene in the ACW; they were thwarted by a combination of the British Fleet and the overwhelming superiority of the American Ironclad Monitors in brown water combat vs. wooden hull warships. The British actions (which were based more on opposition to THEM then love of the U.S.) has the effect of starting the "Special Relationship" 70 years early.
After the ACW ends as in our TL the United States invokes the Monroe Doctrine because of the THEM sponsored occupation of Mexico (OTL Maximilian Empire). THEM fleets attempting to support Maximilian's forces are interdicted by American naval forces. Vera Cruz is taken by American Forces to prevent resupply and the Mexican resistance army receive material & moral support from both the U.S. & U.K. Both English speaking nations offer military Volunteers to the underground Mexican government, however the Mexican forces, while grateful for the weapons & money, has no desire to trade one foreign army for another. In 1866 Maximilian is captured, tried & executed as an enemy of the state. Within 3 months US forces have evacuated Vera Cruz, although US & British naval squadrons, often under joint command, maintain a close watch on the Gulf of Mexico.
In 1880 the United States which has never completed demobilized it's fleet & Army (as happened in OTL), blockades, invades and captures ALL Spanish, French, Dutch & German Islands in the Western Hemisphere. U.S. & U.K. forces take French Guiana in 1884. THEM attempts to sieze Gibraltar in retaliation but are repulsed.