Gothic was the first language that J.R.R. Tolkien studied for his own pleasure, and it may have given an impulsion in the first development of Qenya. Tolkien even attempted to reconstruct some parts of the language and such elements survived in Taliska, the language he created for the Edain of the First Age. He also composed a full poem, Bagme Bloma "The Flower of the Trees" in Gothic.
Since in Lord of the Rings Old English represents Rohirric, Tolkien used Gothic to represent the earlier language of the Northmen of Rhovanion in order to show the relationship between these languages. However, in reality Gothic had no descendants, so Old English is not directly related to it; therefore this simulation does not reflect exactly the relationship between Northern and Rohirric.