*bump*
Perhaps a Fashoda war with a Franco-Russian (plus China) alliance against UK-Germany-Japan is the best option.
I don't think Russia would care very much about what happened in Fashoda.
I think the two best bets for war are either:
1. War over Central Asia {ie. India and Afghanistan}
2. War over Istanbul
1 is unlikely as I don't think Russia actually wanted India. So the best bet for war is over Istanbul and the Straits. I assume that such a war would take place in the early 1900's.
French Reaction: France is caught between a rock and a hard place. On one side, they need to keep friendly with Russia in order to keep Germany on her guard. On the other, they need to keep friendly with Britain for kind of the same reasons. Assuming everything else is the same as OTL, I say France sides with the British. If you want to see France take sides with Russia, heat up the Anglo-French competition in the Scramble for Africa. They actually nearly came to war over the most unimportant places on the continent.
German Reaction: Sides with Ottomans, doesn't want to see Russia increase in strength.
Japan: Doesn't care.
Austria: Side with whatever side the Germans are on.
Italy: Sides with Britain, no reason to side with the Russians and probably doesn't want a Russian presence in the Med.
Now of course, when I say "side with" I don't mean "fight with". I don't think this will explode into major war.