We'll go with the Napoleonic conquest here...
Firstly, I very much doubt such a conquest would take the whole island decisively. The enmity between Britain and France is long-standing, and I can't see acquiescence on any long-term basis - particularly if Napoleon's European client states are anything to go by. There's always going to be a low- or-high-level anti-French mood whatever happens, and at the first sign of Imperial weakness you'll get anti-French activity.
I can't see the Napoleonic empire ever being so secure that Britain could be left ungarrisoned. Expect partisan activity in the countryside for two or three generations, assuming the empire survives and thrives.
Most likely, British governance would be entrusted to a collaborationist government at arm's length, backed by a certain number of French occupying forces. If Nappy can persuade George IV to stay on as a puppet, all the better - it rules out legitimist British restoration movements, and maintains the veneer of British sovereignty. Even at the highest levels, though, I doubt there would be any large scale adoption of French culture. Instead, you'll see the dominant cultural force being a passive British nationalism - not only as a reaction to the aforementioned subjugation, but as a way to emphasise the regime's legitimacy by ideologically placing it as far as possible from France.
At the lower level, the easing of trade restrictions with France might bring a certain level of French material influence to life in Britain. Wine becomes cheaper and more widely available.
What would happen is that Ireland would be gifted her independence much earlier, and possibly set up as a Bonaparte client state. If there's Francophilia anywhere in the British Isles, it'll be in Ireland - expect the Irish middle classes to enthusiastically embrace all things French post-independence.