Synthetic is something not real. Of course English is a real language even though its roots lie in other languages.
"Synthetic language" is a technical term in linguistics, and has nothing to do with whether the language is real or not. Simply put, synthetic languages are languages that cram lots of morphemes into few words. English generally does not fall into this category; instead, it is what is called an analytic language (i.e. its has few morphemes per word).