I can't see that happening. In this scenario, Austria and Russia would still have conflicts over the Balkans while Austria has basically no territorial conflicts with either Germany or France. If there is a Franco-German rapproachment, I imagine that the more likely outcome is a Paris-Berlin-Vienna(maybe -Sofia and/or -Constantinople) alliance opposed by Britain, Italy, Russia, and some Balkan countries, none of whom have the power to take on this alt-Central Powers/Entente by themselves and I have doubts that they could do so together either, especially since there are conflicts between Britain and Russia, and Italy would have to be quite suicidal to join such a war since its surrounded on all sides and none of their potential allies border them or are otherwise close to them.
If there's a Franco-German reproachment to the point of an outright alliance, it throws OTL dynamics out the window. There may not even be any solidified alliance blocks, just shifting games of influence over the states of Europe between Britain, Germany, Russia, and to some extent France. This is Bismark's dream- Germany is the strongest European power, but there's no impetus to cut them down to size, or large alliance forming against them, just some geopolitical calculations. It is also an acceptable arrangement for Britain, who is happy to see no continental hegemon. Certainly Italy can do nothing against Austria, Germany,
and France if the three are truly cooperating. Colonial disputes get thrown more into relief in this Europe, with the Great Game in Asia and conflicts between France and Britain being more important.
Could such a state stick around forever? Probably not. There's still that drive within Germany to take their "place in the sun" and become the dominant European power. Russia will, starting in the early 20th century, begin to grow, and challenge Germany's status as the "first among equals" of the European great powers. I bet tensions will start again as the Ottomans decline, and a scuffle in the Balkans could escalate to create more formalized alliances.