Is there a known language with the same grammatical structure as English?
Why, that’s a very ambiguous question. A “grammatical structure” tends to be one specific aspect of a language’s grammar. If you mean a high level of grammatical similarity to the English language, most languages have at least a few differences from any other given language, no matter how closely related they are. As the other answerers have stated, English’s close relatives tend to have similar grammars. Scots (an endangered Germanic language spoken in Scotland) is English’s closest relative, and has an almost identical grammar at the basic level. Frisian, Dutch, and Afrikaans also share many characteristics, as they are closely related to English. For the most part, most Modern Germanic languages (with the exceptions of Icelandic and German, as they both retain a number of archaic features which have fallen out of use in other Germanic languages) bear a strong resemblance to English, when speaking in terms of grammar. The influence of Old French on the English language is irrelevant