I don't really doubt that, though it's unlikely that the army in question will be waiting for the Russians to wander into their arms, I think it would be a surprise. If there is someone partially competent leading that Russian force, maybe they can raise the locals and make things interesting.
Would they be able to transit a substantial force through Afghanistan and have their arrival in India be a surprise? I would have to imagine upon the declaration of war British India will begin to mobilize, even if slowly.
 
So
UK, Germany, AH vs France, Russia, Italy, Spain ?
former wins defeats the latter totally right ?
Doubt it, Wilhelm was an idiot when it came to foreign policy, he wasn't a great diplomat or statesman similar to Bismarck, Britain and Germany are an unlikely Match because of this, and fi the war drags on into 1901 and the Queen Dies, what happens then? Wilhelm might claim the British throne because of his minor Birthright, and boom another conflict. Austria-Hungary was weak internally, it wasn't that centralized and it had ethnicities waiting to jump it and stab the already leaking Balloon Austria-Hungary was, Romania and the Ottoman Empire would intervene depending on what Abdul-Hamid deems as necessary. On the other hand, Italy and Spain where poor and face political and internal Problems, both of which lacked a powerful Military or strong Navy, the only feasible power is italy, which recently was defeated by the Ethiopians some years before. Russia wasn't really industrialized, however I can see its leadership being somewhat better from 1914 Standards, as much of the Russian Generals, by 1914, had rivalries because of the Russo-Japanese conflict. Japan would stay neutral since in this OTL the Boxer Rebellion most likely doesn't happen. With France its not as industrially capable as Britain is, it lacks coal reserves in its mainland and its Fleet isn't up to Parr with the British Navy, However its land army wasn't so bad, in fact had the upper hand until the early 1900s, I could see the French experiencing Marginal victories against Britain and Germany on Land, after all, it came a long way from 1871 and had superior leadership and a better artillery corps. This is probably why the Fashoda incident never really took off, both powers where powerful in their own right, however in the end its most likely a draw due to Poor diplomacy and the declining health of Queen Victoria.
 
Interesting how much talk this premise has generated about Germany and offensives against British India, but speaking about the Scramble for Africa, and a conflict rooted in the Fashoda War, I would expect a conflict centered in Africa.

A Fashoda war would start over South Sudan and its central antagonists would be Britain and France, with the other powers as bit players or sitting on the sidelines.

An escalated war would radiate out from Eastern Africa. The immediate prize for the victor would be the Eastern Africa region, with colonies like Sudan, Chad, Equatorial Africa, Djibouti, Somaliland, Uganda, and Kenya at stake.

A decisive win in an escalated war would see much of pink British Africa turned French purple, or French purple Africa turned British pink. I suspect, given British clear naval superiority, than English pink will predominate over much, much more of Africa, so there will be a big purple to pink shift.

If Britain makes a total clean sweep of the oceans and seas against the French, Britain can wipe all the purple off of Africa.

But that would be quite dramatic, and the French probably could be competitive in the Mediterranean, and have pockets of substantial military strength, especially in North Africa, like Algeria, and West Africa like Senegal, so perhaps, the Mediterranean coast of Africa from Algeria or Morocco to Egypt could end up French dominant, with Sub-Saharan British dominant. Or the split could work out some other way.

The other place where large British and French colonial territories meet is the border of Indochina and Burma in Southeast Asia. Clearly, Britain can raise far more troops from India than France can from Indochina.

As others have mentioned, France's ally, Russia, can theoretically threaten British India, but logistics and terrain mean they can't project large numbers very far very fast. The Russians I imagine could leverage British preoccupation to gain a good upper hand in Persia though.
 
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