Well Britain and France got on quite well during the 2nd French Empire between 1852 and its destruction in the Franco-Prussian War. Napoleon III opened up the French economy to cross channel trade believing that it would force French industry to be more comparative and hoping to use lower cost British industrial goods to build up the French infrastructure such as the french railways. Then in the 1850s the French and British foreign policy aligned during the Crimean war. Napoleon III wanted a victory under his belt to boost domestic support and to take the place of the primary protector of Christians in the Ottoman Empire where it had been historically been considered the Russian Empire. Britain on the other hand had been concerned about growing Russian power and hoped to contain it, having at least to some extent competed to control Afghanistan to secure the frontier of the British Raj.

With the 3rd Republic arising in 1870 Anglo-French relations mellowed again. Particularly in the late 19th century there was some tense moments between Britain and France over colonial ambitions. Most notably the Fashoda Incident in 1898 in which both countries hoped to secure the Sudan and France was eventually forced to back down. So really British and French interests didn't really realign until into the 20th century, between 1898 and 1901 Britain considered joining the Triple Alliance alongside Germany, Austria and Italy.

It wasn't until 1904 they signed the Entente cordial which still wasn't a military alliance so much as a declaration of friendship, both agreeing to remain neutral in the Russo-Japanese War as Britain was allied to Japan and France Russia with the two sides agreeing to recognise certain colonial possessions as being in the other's sphere of influence. The ground work necessary to stabilise their relations and avoid future fairings of new rivalries over colonial processions as they had in 1898.

This relationship became stronger over the next few years as the Anglo-German Naval Arms race heated up the the Dreadnaught race as HMS Dreadnaught was built in 1906. This new for of battleship virtually made all other battleships obsolete over night and although this meant that Britain was now in possession of by far the most powerful battleship in the world it significantly levelled the playing field for anyone who hoped to challenge British naval supremacy given everyone's battleships were outdated by the creation of dreadnaughts. And the country that tried the longest and hardest to out build Britain was Germany. Between this and German conduct in the First Moroccan Crisis Britain began to be concerned about German power which in part lead to the Triple alliance as Britain decided to put aside its grudges with France's other big ally, Russia.

But as I say this still wasn't a military alliance. The Triple Entente become known as an alliance in the First World war but it didn't obligate Britain to join the war to protect France or Russia, it was the invasion of Belgium that did that. Britain might have joined the war at a later date of course. This was bound into a fuller alliance in September when Britain France and Russia agreed not to conduct a separate peace.