Nothing like the Norman Conquest or The Great Vowel Shift occurred in Dutch. Although from 1795 to 1813 the French occupied the Netherlands and French was the official language in that period, apart from importing a great number of French words, nothing drastic happened to the Dutch language. The history of the Dutch language over the last centuries is more a matter of lending and borrowing vocabulary. Many French, German and English words have been imported from our neighbours.
On the other hand it may surprise you that there are more than 2000 words of Dutch origin in English, many of them from the 17th century when the Dutch sailed all over the world attempting to acquire more colonies. Many words from the maritime trade (dok = dock, boei = buoy, wijting = whiting, jacht = yacht, vracht = freight, kielhalen = keelhaul), from painting (ezel = easel, landschap = landscape, ets = etch, schets = sketch) are of Dutch origin. The Dutch assisted the English in the American Liberation War and left words like koekje (= cookie), koolsla (= coleslaw), Yankees (from Jan and Kees) and daalder (now dollar).
In South Africa, also a former Dutch colony, the Dutch left a whole language, Afrikaans, based on 17th Century Dutch and since then quite simplified. Famous words: aardvarken (the first word in most English dictionaries), boer (= farmer), baas (= boss), and (unfortunately) the most famous Dutch word all over the world: apartheid.