The biggest influence, and this is true of anywhere in the world, will be the US. Too much has to go too right for too long for China to propel itself past the US in the timeframes most people envisage. The US will be THE major power for some time to come.
Russia is looking to regain its Soviet former glory, but it is facing a demographic crisis (Islamification), a population crisis and an economic crisis. Further, there is no guarantee and very little hardware to stop China turning much of Siberia into a defacto part of China.
If the Ukraine can gain access to energy from any source other than Russia it may assume a larger role in Europe, but until that time it will rely on the interests Poland, Germany and Russia to maintain their independence. Roughly the size of France and with a similar population it could be the breadbasket of Europe with the right investment.
Poland is the only Eastern European nation likely to challenge for a leadership role in Europe. It has to get past a generation of political, economic and criminal corruption before that will happen.
Spain and Italy are too backward politically to offer the stability required for a European-wide role. No other nation has the size, population or political/diplomatic establishment to come close to Germany, France and Britain.
Britain gains far too much from its roles as No1 US ally and head of the Commonwealth to ever seriously contemplate a full share of Europe. Because it can't/ won't take that full share it must ensure that neither of its rivals gain too much from a position of leadership. It may support common military and foreign policy goals but British Military thinking is very different to France/Germany and European Foreign Policy is much too soft for British interests.
France gains far too much economically from the current arrangements which prop up its inefficient economy and helps its governments to avoid implementing long overdue reforms. Its attempts to form a French version of the Commonwealth or a Mediterranean league are nothing more than attempting to shore up French political influence in the face of continued German economic expansion. The French military desperately needs updated tanks, small arms and artillery, and none of its home made systems comes close to matching German or British equipment but neither can they simply 'buy foreign' so the military keeps falling behind.
Germany's needs would be better met by casting off the old EU and the drain of the Common Agricultural Policy and create a Mitteleuropa. France uses the historical memory of German policies in WW1 and WW2 to remind the rest of Europe of the dangers of allowing a strong Germany go its own way. it also has an imbalance, politically and economically, with the integrated East Germans. But the biggest break on German power is the strength of the Greens and Socialists and their ideological commitment to peace at all costs.
There is no threat now or likely that will ever draw these three away from their separate foreign policy commitments and ideals to form a tripartite government of Europe. Without all three committed, any one can create enough doubt in the smaller nations to stymie any effort at closer integration.