There is a project which is studying the DNA of HARRISes (and all variants) around the world at http://www.harrisdna.org/http://www.harrisdna.org/
Its aim is to give genealogy researchers direction in finding their origin, which is often difficult with a common surname such as HARRIS/HARRISS/HARRIES. Note that before 1800 spellings often changed as people moved and so many people with the names HARRIS and HARRIES may be related, especially if their ancestors came from near the English/Welsh border.
Take a look at the URL and decide for yourself. At minimum you should do the 37 marker test which, as well as seeing if you are related to any of the existing groups, will broadly categorise your DNA as Anglo-saxon, Celtic, Norse Viking, etc. As most HARRISes originated from France/Britain/Spain most will be anglo-saxon but you never know, you could be more exotic!