Small nit-pick: the traditional enmity was between the English and the French, not the British and the French. Scotland was a traditional ally of France in the Auld Alliance, which started in 1295 and was of practical relevance until 1745, although theoretically terminated in the 1560's.

Up until the end of the 19th century England was fearful of France. And rightly so, in their eyes. France and Russia had allied, had the 2nd and third largest navies in 1898, with 17 and 11 battleships respectively, and France was beginning to spread her empire into British spheres on Influence in Africa; See Egypt and then Fashodan crisis in 1898.

Diplomacy came to rescue with relations between France and Britain, but not due to friendly relations, but due to Germany's failings on the international stage. Germany was pretty poor when it came to diplomatic talks, and the friendship between Britain and Germany soured rapidly between 1898 and 1914, as Germany built up her Navy and began to cause mischief in Africa. The Moroccan crisis, where German naval forces turned up on the Moroccan coast claiming German right to control Morocco. They quickly left when a British naval force, that bit bigger and more powerful, arrived to defend the French.

Add to this Germany's aggressive naval expansion, the Navy Laws 1989-1914, which saw German battleships increase from 4 to 31 in 16 years, put great pressure on the naval status quo and control that Britain had.

Both France and Britain ad a joint issue with this. It endangered the free trade routes they had in the North sea and channel, and so Britain made a very clever deal with France. France would defend British area in the Med and Britain will move the bulk of her naval power up to the North Sea and Channel and if any power attacked France from sea Britain would defend.

French relations with Britain were always tense, but the rise of Germany in the later years of the 19th century saw the two pushed close by fortune and a common threat, not necessarily a common enemy.

Also, Russia's naval threat completely collapsed following the Russio-Japanese war saw they were no longer a threat and France became little to no threat. They even pulled out of Egypt and recognised it as British.

Sources

W.Podmore, British foreign policy since 1870 , (London, 2008)

S.T. Grimes, Strategy and war planning in the British Navy, 1887-1918 (Woodbridge, 2012)

B.M. Gough The Royal Navy and the northwest coast of North America, 1810-1914 : a study of British maritime ascendancy, (Vancouver, 1974)