http://andromeda.rutgers.edu/~jlynch/language.gif
That Norman invasion was a big deal.
In reality, lexical analysis of Romanian shows that it has the following roots:
* pre-Indoeuropean (some words with unknown origins, just a handful, but still)
* proto-Indoeuropean (another small bunch of words)
* Dacian/Thracian (original Indoeuropeans to settle the region; another somewhat small contribution)
* Latin (40% but basically the core vocabulary)
* Slavic (30%, especially nouns, but rarely verbs)
* French (around 20%, imports from the late 18th century onward)
* German, Turkish, Hungarian, English, etc.
So, you were saying? :) Even if you disregard the minor contributions, there's 2 prehistoric origins (pre-Indoeuropean and proto-Indoeuropean), 2 ancient origins (Dacian and Latin), 1 major medieval influence (Slavic) and 1 major modern influence (French).
The European continent had waaaay more invasions than the British Isles, don't forget that ;)