Well, actually things are quite different. All indo-european languages, including english relate back to proto-indo-european, that is the mother tongue of most of modern languages. Also sanskrit (together with latin, greek has evolved from this very ancient language, but belongs to different branch of evolution.
English as well as German are both modern languages that belong to family of Germanic languages. Both are West-Germanic languages. English belong to Island-German branch, where as german and dutch belong to High-German branch. Other languages in this family include swedish, norvegian, danish, that belong to North-German branch.
English is as closely related to sanskrit as german. Only thing is that german language has wider sound inventory, including a lot of consonants that are pronounced in same way as those excisting in sanskrit. Sound inventory of german language is wider than that of english and german spelling is nearly phonetic, where as english spelling is far from logical.
It is true that german speaking person can pronounce sanskrit words with less effort than a person with english background. But it does not mean they would understand the language. It only means that some of the sounds and phonem combinations existing in german languages are similar to sanskrit.
Among indo-european languages the Baltic and Slavic branches are perhaps most closely related to sanskrit. Such languages as Lithuanian, Lettish and Russian. Czech & Polish have quite a lot of words that relate back to sanskrit. Modern hindi, bengali, punjabi and other indic languages relate directly to sanskrit. Persian languages, including Iranian and Kurdish belong to same Indo-Iranian main branch as Sanskrit and modern Indic languages.
See Wikipedia about germanic, Indo-European, Sanskrit
Here is one presentation of indo-european languages: