That, and invasions. Quite substantial parts of Europe have spent hundreds of years under rulers from a country with a different language, who'd often mean aristocrats and bureaucrats and military with a different language.
English is the prime example of the effects of this, with it's French/Germanic split (French from the Norman aristocracy).
The French may have originally started to trickle in to English from Norman French, but Norman French and Central French differ greatly and most of the Central French in English actually came much later due to French being a prestige language with-in Europe. The Latin and Greek also came through a similar mechanism, though more because they were scholarly. The idea that Norman French is the source of all English French loans is pretty easy to prove with comparison - Warranty vs Guarantee, liquor vs liqueur, hostel vs hotel, castle vs chateau, catch vs chase, warden vs guardian. Some could equally have come from earlier borrowings (e.g. hostel vs hotel), but the same happens when you compare any two dialects of the same root language (i.e. Norse and Old-English dialects), so nothing is 100%.
You're of course right - I'd entirely forgotten about the later wave of French influence.
Of course that also to a large extent spread via the upper classes first and foremost..
There's a saying I first heard about Danish - a bastardisation of a quote often misattributed to Charles V - about how aristocrats would read Latin in books or use it at court, speak French to the ladies, German to his dog, and would only speak Danish to servants.
The exact set of languages (and animals...) differ in different versions of the saying, but generally it puts Spanish, Italian or Latin at the "top", then French, German and sometimes finally a local language.
In french there is a common pattern where words lost an "s" while a vowel gained a circumflex. i.e. hospital -> hôpital, forest -> forêt, etc. I'm guessing hostel -> hôtel is another example of that pattern.
