With one half of the political spectrum discredited, France's navy will get a consistent policy in the early 20th - which they sadly lacked IOTL. Moreover, if significant naval action occurs - and goes poorly for France, she can spend more money on new construction and less on maintaining obsolete/obsolescent ships. With Anglo-French tensions high, one might see France producing a Dreadnought first, and at least one can expect a swifter than OTL response to any RN construction of same.
The Army, however, might end up worse off. The left had been concerned about the Army's monarchist sympathies since the war with Prussia, and insisted on keeping it on a tight rein. If the Army is discredited by fighting a war badly, it's quite possible that the government would make none of the moves that helped the Army to improve its higher command structure IOTL. That said, in this sort of situation, the government might be more inclined toward a defensive posture, and insist on its military theorists and industry supporting such a posture. So more machine guns, more heavy artillery, light mortars and so on - but perhaps at the expense of corps and army-level command structures, as I suggested before.
In that sort of atmosphere, Franco-Russian military talks are unlikely to proceed as we know them. IOTL the two armies gradually agreed to launch major assaults into German territory swiftly after the declaration of war. But with France's government wary, we could instead see the French army awaiting the Germans, and covering the frontier with Belgium in strength as well. Obviously, in that scenario, the Russians almost certainly won't be attacking either. Not Germany, that is. I imagine they would still take the offensive against A-H, probably with much the same initial results as IOTL.
The initial outlook is more promising. Russia has suffered fewer casualties for much the same gains as OTL. She has no need to hurriedly gather troops in Poland to replace Rennenkampf and Samsonov's armies, and can instead send these reinforcements and supplies to the A-H front. This might be sufficient to knock out Przemyśl by October '14, leaving Russia in a good position against A-H for the spring of '15.
France, meanwhile, has caused greater casualties and probably lost less ground than IOTL. A greater inclination to defence has probably led to the protection of the industrial sector lost IOTL. I assume that the weaker French staff work ITTL won't be a major problem when on the defensive, but it frankly could be disastrous. However, assuming it isn't, France has more men, more materiel and is in a better position than IOTL.
However, she does not have British financial and industrial support. The loss of British manpower will also become steadily more significant as the years of war wear on. In short, taking the offensive will be even more perilous than IOTL. It's worth noting that ensuring Russia stayed in the war was a prime consideration for the Entente IOTL, and was a major factor in many of the attacks sometimes dismissed as futile. If Russia feels she is pulling all the weight, she will be displeased.
The Mediterranean and North Sea are interesting areas. Quite how bad Franco-British relations are will decide to what extent London elects to neuter the High Seas Fleet by forbidding operations in the Channel, say. Meanwhile, in the Med, the two interesting questions are Italy and the Ottomans. Italy can go either way in a situation like this. One can say more, but that's the short version.
The Ottomans, however, are more likely to stay neutral or even to join the Entente. They did seek an alliance with Paris mere months before war broke out IOTL. France rejected them for fear of angering Russia, always eager for control of the Dardanelles. But ITTL the French strategic situation is weaker, lacking British support, so there's a fair chance they may make some arrangements. Perhaps a full alliance is still out of the question; I couldn't say for sure. But an understanding of neutrality and friendliness seems achievable. This would mean that Russia would not be cut off from supplies passing through the Black Sea.
If Britain (and thus other nations) similarly insists on trading with all belligerents for her own financial benefit, then nobody is going to run out of shells and cartridges soon. Though mention should be made that if the Haber Process is butterflied away by a short time and the Germans fail to secure OTL's nitrates stockpile, then they'll be hard-pressed to do any shooting at all without large imports from other nations.
Not a comprehensive analysis, I admit - very Eurocentric - but it covers much of the major stuff, I hope.
