The short answer is Entente Cordiale in 1904, which means the alliance between the two is just now a century old. Prior to that, the two powers were certainly at odds, and this rivalry was critical to the development of each nation-state (I am thinking of Linda Colley's Britons as one example). As Richard Mayne notes in his collection Cross Channel Currents, the entente cordiale was not the first agreement between Britain and France but certainly the most effective and enduring, as it helped to create a great cooperation between the two. Still, the Great War played a pivotal role (as Britain was brought into the war not by the Entente agreement but rather by the Treaty of Belgium (at least according to diplomats at the time) in cementing the relations between the two states as one of cooperation.