EU definitely has potential but frankly speaking - I don't see it happening.
EU doesn't have a fiscal policy as a whole nor they have military outreach as significant as USA. Biggest problem is the countries constituting EU are at different bandwidth - political stability, market stability and growth and debt wise.
USA despite their hard hand approach of using dollar as a weapon still has a massive military outreach. And, most of the present Global debt is in US dollars as well.
If US dollar share as global currency goes down, then I don't see any currency dominating the global market like USA did - each major currency would try to have some pie - Like China, EU, UK raising their shares and US would still try to hold some significant share to not let go of complete control