The easiest answer to give is: the existence of a European power that poses more of a threat to both France and the UK than the two pose to each other. It's not like France and the UK were never allies even counting pre-Entente: they teamed up against the Habsburg Empire of Charles V and subsequently against Spain and the Netherlands.
Of course, alliances in the face of mutual threats are probably not the same as solid alliances - I assume you probably want the sort of cultural exchange that occurred between France and the UK post-Entente.
I can think of several PODs that could produce longer alignments that, over time, would result in greater linkages between the two countries:
1) The Habsburgs replacing their marriage policy for one that doesn't result in such a terrible genetic outcome. Even if it does nothing to improve Spain's prospects in the medium-run, continued Habsburg rule over Spain would likely result in a continued Austria-Spain axis, which would be more likely to generate a counterbalancing England/UK-France axis.
2) Had Louis XIV managed to save James II in the Glorious Revolution, that could well have created a Catholic Franco-UK axis against the other members of the Grand Alliance (esp. as James II would pretty much be at the mercy of the French).
3) The Metternichian system fails catastrophically post-1815 (maybe with a more insistent Alexander I of Russia pushing his goals in cooperation with Prussia), which would initially likely result in a counterbalancing alliance of Austria and Britain but will eventually probably see France substituting for Austria as the latter's domestic politics become increasingly unacceptable for UK liberals.