Mexico helps the Confederates (CYOAH!)

The Mexicans were in no state for war against the Union, and also the rest of the world, but they, holding a grudge after Texas and California, join the Confederates. It is a fragile alliance, what with Texas being in the CSA and all, but the Mexicans begin an advance. France, seing this, decides that the 1000 year rivalry between Britain must end, and that Mexico would make a great spoil of wa. Thus France states that the Republican ideals were against a war with the United States, and were more than happy to liberate their fallen allies, such as Ireland and Scotland. The French land in the coasts of Mexico, but the Mexicans resist for a short while. The UK attempts a landing at Normandy, but fails. The French begin an Atlantic wall, digging in for any British attack. Soon all of Europe has fortifications surrounding its coasts. The US, on the other hand, begins a push deep into Mexico, hoping to surround the Confederacy. The Mexicans, seeing that enough is enough and that they need to surrender to live on, sign an armistice. They begin to join the war with the Union in exchange for Texas, but giving up Baja California and some slight border territories. The Confederacy surrenders, and only Britain and its colonies remain. What does Britain do?

Do they...

Give up, stating that the reason they joined the war was no longer applicable

or

Continue until the last Brit dies.