Gunpowder, also known as black powder, is some nasty stuff. It's extremely corrosive, it produces large amounts of obstructive grit and fouling, and using it creates a cloud of obscuring smoke.
So when Poudre B was invented in 1884, this was a big deal- suddenly the great powers of Europe had access to a cleaner, more powerful, easier to handle propellant, and the immediate result was a massive improvement in the effectiveness of small arms and artillery. It also paved the way for the development of effective self-loading firearms, since it fouled much less than black powder and burned more consistently.
But suppose more effective propellants had never been invented, and at the outbreak of hostilities in 1914 all the actors in the First World War were still armed with black powder weaponry. Would this significantly change how the war was fought?
From my research, I have found a few points for and against.
Infantry small arms developed prior to the First World War were designed to be effective at very long range, using pointed 'spitzer' ammunition and high velocities to have lethal ranges of up to 2-3km. While this proved impractical, and most infantry combat took place at an effective range of well under 500m, machine guns were able to provide plunging fire support from a kilometer away or farther. The lower muzzle velocity of black powder projectiles would reduce range, and fouling in the barrel would quickly reduce accuracy under sustained automatic fire.
Artillery, which dominated the war, was dependent upon cordite-based propellant to maximize range. Reduced artillery range would have put artillery closer to the front lines, increasing its vulnerability to aircraft, as well as infantry overrunning the protective trench network.
Tanks would be more difficult to damage and potentially have a larger impact on the war, owing to the lower muzzle velocity and corresponding penetrative ability of all firearms in use.
For the same reason, body armor might be more effective. While armor capable of stopping rifle rounds was tested (example: Brewster Body Shield), it was excessively heavy and cumbersome. Less armor penetration from the ammunition used would mean less armor needed to stop it.
The development of pointed bullets in the first place was a response to bullet deformation associated with the higher velocities attainable with cordite propellant. A lack of better propellant might have delayed the development of pointed bullets and resulted in traditional round-nosed bullets being used, which due to their poorer aerodynamic and armor-piercing capabilities would exacerbate all the effects mentioned above.
The fouling of black powder would noticeably impact all automatic firearms. Blowback mechanisms, like those used in self-loading handguns and submachine guns, would experience greatly reduced reliability, which may delay the deployment of personal automatic weapons like the MP-18 to the battlefield. Gas-operated mechanisms such as in the Browning Automatic Rifle would likely be unusable- numerous videos on Youtube (example) show how rapidly a modern gas system clogs from the byproducts of black powder. Most importantly, this would severely reduce the long-term reliability of machine guns, leading to more frequent stoppages during sustained fire.
The amount of smoke produced by black powder could easily obscure a battlefield and prevent long-range fire altogether. Accurate fire during Napoleonic-era warfare was difficult enough due to smoke (example), so I can only imagine how difficult it would be to fire accurately at 200+ meters at the rate of fire provided by bolt-action rifles, let alone machine guns. This more than anything else might limit the effective range of engagements.
The combination of all of the above could possibly prevent cavalry from becoming obsolete. Practical body armor, less effective machine guns, and greatly reduced effective range might reduce cavalry's vulnerability to infantry, and allow them to continue to fulfill the rapid breakthrough role that in the real world would eventually be filled by tanks. The preservation of maneuver warfare could help to avert the stalemate of Western Europe.
Information on the Lee-Metford rifle in .303 British, which was used with both black powder and cordite loads, indicates that the switch from BP to cordite only increased the muzzle velocity from 1850fps to 1970fps, an increase in kinetic energy of only 13%. This suggests that the difference in muzzle velocity might not be substantial enough to have the kinds of effects I described above.
Trench warfare was already in development long before the development of smokeless powder. At the Siege of Sevastopol in 1854 as well as the Battle of Antietam in 1862, field fortifications proved instrumental in protecting infantry against hostile fire. Even with the obscuring characteristics of smoke, this would suggest that some form of trench warfare would still exist in a black powder-only First World War.
While black powder fouling might prevent blowback and gas-operated firearms from functioning, recoil-operated firearms that minimize the amount of gas released into the action might continue to function. The earliest Maxim Gun prototypes were designed for black powder, and Maxim himself filed patents for devices to reduce black powder fouling in automatic firearms. It is possible that with another thirty years of development before the outbreak of hostilities, machine guns could be developed to function reliably on black powder.
Ultimately, artillery accounted for a majority of the casualties inflicted over the course of the war. If black powder was close enough in effectiveness to cordite for artillery purposes, the effects on small arms might end up being irrelevant.
What should the net effect of a lack of smokeless powder be? Would this radically change the course of the war, be a minor technological discrepancy with trivial effects, or somewhere in between?