I sincerely doubt that the euro can become the new reserve currency, not only because the US will use all possible means and methods to prevent that from happening, but also because the EU is simply too weak politically and militarily to be able to raise its currency to such a level.

Looking further ahead, after the UK leaves the EU all that needs to happen is for another major country to do the same and the foundations of the EU will be quite shaken. If you look at the overall picture, it is difficult for the euro to replace the US dollar, no matter how bad the latter is at the moment.