I have made beetroot wine before, but I wouldn't really call it a wine more of an Aperitif. It's very earthy, and quite fragrant (due to the recipe I followed which included some spices). Even without the spice I don't know if the 2 ingredients (Beetroot & Blackberries) would work well together.
I'm not trying to dissuade you, but if you are simply thinking of this recipe as you are short of blackberries then I would say some other dark fruit might be a bit more complimentary i.e. Elderberries, blackcurrants, possibly even cherries spring to mind. If you just fancy giving it a go then keep us posted.