JJ: I can tell you that a German who has never learned English is absolutely unable to unterstand English (the same is true of course for the other direction).
The fact that many words have the same origin does't help very much. You cannot not grasp the sense of whole sentences. The chance to understand some single words my be higher for written texts as dogboy alread mentioned. But nevertheless: An English or German person will not be able to unterstand a text in the other language if he doesn't have any training.
BTW: English has more words of french than of German origin. But the most basic words are nearly all German which makes it near to impossible to build a complete English sentence without using "German" words.
I don't believe that you think that somebody who speaks and understands Englisch can unterstand French?!