I think most things have already been covered by people here, but a few thoughts;
Fashoda in itself isn't enough to get a war out of. Marchand was too isolated (and sensible) to do anything helpful or remotely threatening, Salisbury had no particular desire to provoke a conflict if he could avoid it, the French knew the whole thing was a losing proposition, and were distracted by the Dreyfuss Affair anyhow. Worst-case scenario (which would be reasonably interesting in itself) is that there's a confused, silly skirmish in the Sudan, Marchand surrenders after a few deaths, and that's as far as it goes.
To get a proper war out of it you need to up the ante somehow. Ways of doing this include giving France a proper ally (ie Russia), combining the crisis with another colonial clash to make the thing seem like a coordinated attack on British interests, boosting the power of the French force in the Sudan (and the only way to realisitcally do that is by making some of the OTL intrigues to get the Abyssinians to send an army to the Nile come off), and giving everyone more belligerent leadership.
In "Fight and Be Right" (which I think is the only TL do deal with this, and the subsequent war in detail, instead of quickly moving on) I basically did all of these things. I also had to give the French a bit of a military leg up to make it a slightly fairer fight (the British still win).
So for the sake of argument, let's say the ducks are lined up and war breaks out, not only in the Sudan but formally, between Britain and France. What happens next?
I suspect it's rather a dull war. The French Navy at this point was a complete mess; they were averaging a Marine Minister a year, and this lack of stability meant that ships were cancelled half-built or delayed for years for political reasons as new incumbents reversed the decisions of their predecessors and then their replacement ressurected half the things they'd abandoned. The result was a Navy full of prototypes and with no overall cohesiveness; that didn't have a proper mission. If they try to go to sea, the Royal Navy (which had by this point recovered from its own doldrums of the late 1880s/early 1890s) will have a field day, and the French know this. More likely, there will be isolated commerce raiding and everything else will stay in port while the British snap up colonies at their leisure.
It might be fun if the Boer War can start anyhow though; the plucky Boer doing what the Frenchman can't might be fun, particularly if the French manage to get them weapons somehow.
But generally? I think it'd last six to nine months, with no major battles and an eventual British victory by default. Delcassé knew this, which is why he ended up conceding; as I say, for a proper war, you need to raise the stakes considerably.
Fashoda in itself isn't enough to get a war out of. Marchand was too isolated (and sensible) to do anything helpful or remotely threatening, Salisbury had no particular desire to provoke a conflict if he could avoid it, the French knew the whole thing was a losing proposition, and were distracted by the Dreyfuss Affair anyhow. Worst-case scenario (which would be reasonably interesting in itself) is that there's a confused, silly skirmish in the Sudan, Marchand surrenders after a few deaths, and that's as far as it goes.
To get a proper war out of it you need to up the ante somehow. Ways of doing this include giving France a proper ally (ie Russia), combining the crisis with another colonial clash to make the thing seem like a coordinated attack on British interests, boosting the power of the French force in the Sudan (and the only way to realisitcally do that is by making some of the OTL intrigues to get the Abyssinians to send an army to the Nile come off), and giving everyone more belligerent leadership.
In "Fight and Be Right" (which I think is the only TL do deal with this, and the subsequent war in detail, instead of quickly moving on) I basically did all of these things. I also had to give the French a bit of a military leg up to make it a slightly fairer fight (the British still win).
So for the sake of argument, let's say the ducks are lined up and war breaks out, not only in the Sudan but formally, between Britain and France. What happens next?
I suspect it's rather a dull war. The French Navy at this point was a complete mess; they were averaging a Marine Minister a year, and this lack of stability meant that ships were cancelled half-built or delayed for years for political reasons as new incumbents reversed the decisions of their predecessors and then their replacement ressurected half the things they'd abandoned. The result was a Navy full of prototypes and with no overall cohesiveness; that didn't have a proper mission. If they try to go to sea, the Royal Navy (which had by this point recovered from its own doldrums of the late 1880s/early 1890s) will have a field day, and the French know this. More likely, there will be isolated commerce raiding and everything else will stay in port while the British snap up colonies at their leisure.
It might be fun if the Boer War can start anyhow though; the plucky Boer doing what the Frenchman can't might be fun, particularly if the French manage to get them weapons somehow.
But generally? I think it'd last six to nine months, with no major battles and an eventual British victory by default. Delcassé knew this, which is why he ended up conceding; as I say, for a proper war, you need to raise the stakes considerably.