The Germans will have the 7.7cm FK 96 field gun (the FK 96 nA with recoil system started entering service in 1904, IIRC). The French will have their modele 1897, a much superior gun, but it only started going into service in 1898, so they probably won't have large numbers of them. Artillery will be less effective relative to small arms.
The German Army adopted the Maxim only in 1908. The French tried a Puteaux gun in 1905, but it was unsatisfactory; the St. Etienne and Hotchkiss were adopted in 1907 and 1909, I believe. So barring significant changes, neither nation have many machine guns in 1900. Britain will have more, having adopted them in the 1880's; not sure of the scale of issue, though, and the small initial size of the BEF will deny any huge effect initially. The other nations will speedily build copies of the Maxim.
All nations had effective magazine rifles, though, even if the designs are mostly not as refined as in 1914. And I suspect that the fire of magazine rifles will be enough to quickly push things toward stalemate -- it may take longer, and the tactical stalemate may not be as ironclad as OTL, until the QF guns and MGs become prevalent.
All nations have the ability to mobilize tremendous numbers of soldiers, and the production capacity to supply them. This results in a large troop-to-front ratio.
The European railway network was quite dense in 1900, so the capability to mobilize, deploy, redeploy and supply the armies exists. Nonetheless, all nations kept building their railroads from 1900 to 1914, especially in the areas they expected they might have to fight; so the carrying capacity in the relevant areas won't be as great as it would in 1914.
One of the reasons that warfare on the Eastern Front was more fluid in 1914-17 was the relative scarcity of railroads; if one side achieved success, it took too long for the other side to bring in reserves. Since the railway network of 1900 was less dense than that of 1914, this factor might well be in evidence. We might see a bit more movement, until the lines are pushed to a point of balance, where the defender is now close enough to his local railway to stabilize the situation.
So the high troop ratio and relative ease of moving reserves will contribute to an operational or strategic stalemate.
We won't see either side sweep so rapidly through Belgium; the massive guns needed to quickly crack fortresses weren't in existence yet.
So I figure you'd see a bit more fluidity on the direct front (A-L and, possibly, the Ardennes) but still ending in stalemate. On the northern part of the front (if Belgium is even invaded), you'd see less fluidity than OTL 1914, ending in stalemate somewhere inside Belgium.
The nature of the stalemate won't be quite as firm, since magazine rifles can't kill at the rate that QF guns and MGs can, and the railway net isnt quite as dense. Once those guns are fielded in large numbers (which will be a priority for everyone), and additional war-built rail links are constructed, though, we get a situation almost exactly like in OTL WW1.
(I'm not considering political factors, nor butterflies resulting from a presumably more tense Pre-1900 period, at this point; but these would have an impact)