You want Russia and France to be stronger than they were in 1914 OTL (when Germany and Britain together could have wiped the floor with them pretty comprehensively). So, very quick sketch:
-Kaiser Wilhelm II falls into a pond as a young boy and develops acute hydrophobia. Expansion of the Kaiserliche Marine is small and conservative.
-Russia wins the Russo-Japanese war: not that hard to do. That, or possibly Bezobrazov and his pig-headed colonialists don't get the ear of the Tsar and Russia recognises Japanese primacy in Korea in exchange for recognition of Russia's own priveleges in Manchuria, which is easier still; but victory makes the Russians look even more menacing.
-So, we've got a Russia that at any rate appears stronger as there has been no lost was disastrous for its prestige, and no 1905 revolution. Russia continues to strengthen its presence in Manchuria, to the alarm of Britain.
-The Russian capitalists, as in OTL, start to obsess over the possibilities of the "Petersburg-Persia line".
Now, this is where I'd want to start cracking open actual reference works and looking at the intricacies of how the R-J war affected diplomacy, but in very broad strokes:
- Franco-German relations still sour.
- French military leaders still become increasingly confident in their own capabilities; defiant pro-Russians become foremost in the French government.
- Less warming of Anglo-French relations. The Entente, as it came about OTL, was in part a result of the R-J war. Britain and France, after Fashoda, had nothing left to scrap about, but changing the R-J war and then the diplomacy around Morocco can keep them at arm's length. No fleet agreements, certainly.
- A deviation from the usual here, but I think the scenario works best if the Ottomans are on the Franco-Russian side, which isn't so hard as it sounds. Russia was always keen on making the Ottomans a client-state, and the French bankers obviously held lots of Ottoman debt. A Russo-Ottoman alliance was actually something people were discussing anxiously just before Franz Ferdinand got himself shot, IIRC.
We have the Ottoman Revolution, the fate of Bosnia, *Illinden, everything we like, to play with here. I think it's possibly to create a scenario in which the Ottomans come to rely on Franco-Russian protection (no 1905 revolution, btw, butterflies the Tsar's relations with the Dashnaks, so if factors elsewhere bring them together, the Russians and Ottomans can be united by hostility to the Armenian national movement, too); and this, with no Tsushima, means Russia is a more credible threat to Britain on the seas.
Then just throw in German insecurities about growing Franco-Russian military power, British popular worries about the straits, and then have some stupid attempt to ovethrow the government in Tehran by one side or the other, and assasinate somebody important. Bang.
It must be remembered that in 1914, the French generals dismissed the military significance of the BEF - in other words, they genuinely counted on winning a war with Germany themselves. Our war, though, need not be in 1914, so the French might have a fighting chance of it.
I'll come back to these sketches in more detail after I've hit the library.