The key points:
The foreign ministers of France and Germany are due to reveal.... Under the radical proposals EU countries will lose the right to have their own army
With Britain gone, France and Germany are by far the most powerful countries in the EU; they would form the bulk of the proposed EU army in any case. They're also by far the most economically powerful countries.
More to the point,
Germany is the economic powerhouse, and
France has (for now) comparable or better military might than Germany. One can easily imagine France and Germany maneuvering against each other behind the scenes to gain ascendance over Europe.
Britain, meanwhile, would have to revert to its old foreign policy agenda of teaming up with the 2nd-most powerful country in Europe as a counterweight to the most powerful. In this case, it might well play France and Germany against each other, and then also work in concord with EU countries like Poland, and possibly Finland and Sweden.
Finally, France and Germany would eventually need to confront Russian expansionism.
The more things change....