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Based on the Russian Army in the Great War Article (provided by LarsBosteen), which seems to analyze the Journals of the 1900,1901,1906-08,10-13 general staff meetings. (Note: it may be necessary to remove the "https://" from the start of the link in order to avoid a 404 error.)
Since this article goes into great details, it can be assumed that Journals/minutes of these meeting were available to the author (N. Valentinov).
The Wikipedia quote that the alliance was amended, is probably false since the article mentions that in the event that their governments decided to help each other in the assumption of war with England.
A copy of the Journal of the 1900 Meeting, Chapter IV, §4 would therefore be needed to verify if this assumption is correct.
Summery of meetings mentioned in the article and the referenced minutes/Journals in the chapter
Extracts from the article (emphasis and minor typographic changes in square brackets added):
Journal of the 1900 Meeting, Chapter IV, §4
The 3rd point of this meeting is 3) Discussion of the program of the agreement against England for action in Asia and Africa.
...
The rest of the meeting was devoted to the consideration of the conditions for the application of the military convention in the event of an attempt Germany to expand at the expense of Austria-Hungary, as well as to consider the issue of joint actions by Russia and France in the event that their governments decided to help each other in the assumption of war with England.
The third meeting on 19 February 1906
As for the reflection at the talks of the two headquarters of the accomplished rapprochement between France and England, it was expressed in a very restrained attitude of the French representative to the question of possible actions against England.
On the categorical question of the [Gen.] Palitsyn, will the French headquarters, in the event of a war against England, carry out the measures that were taken at previous meetings, [Gen.] Brenne said that these measures could be carried out only if a convention between governments was concluded, of which the French staff knew nothing. It should be noted that at the same time the Russian Ministry of Foreign Affairs was, invisibly, just as concerned, in view of the negotiations with Britain, with the desire to eliminate everything that could be interpreted in relation to France and England as preparation for war with England. In the letter to [Gen.] Palitsyn on April 25, 1906, Count Lamsdorf expressed regarding the minutes of the 1906 meeting that “given the present political situation and our significant rapprochement with England,
Note: last reference to England as possible enemy.
[offtopic]
The eighth meeting met in August 1911 with the participation of General Zhilinsky and General Dubaille.
General Dubaille then laid out the French point of view: the French headquarters believed that the first big clashes will occur in Lorraine, Luxembourg and Belgium from 15 to 18 days. France will exhibit over 1.300.000 people. provided by the convention. It is assumed that the Germans will conduct military operations with the greatest energy in order to impose their will on the enemy from the first day and achieve a decision, or at least force the French to go on the defensive. If successful, the Germans will be able to transfer the main part of their forces against the Russians in time. The French army, in anticipation of this move, will be concentrated by Day 12 and will be ready to launch an offensive with the help of the English army on its left wing.
I found this interesting, since this was in anticipation of the Schlieffen Plan almost 2 years before it was officially adopted by Germany in April 1913. Ot also assumed a British participation.
The August 1913 (the last 9th meeting before the war was held) more specific military goals were defined:
This was followed by a presentation of the general principles of concentration and grouping of the French and Russian armies against Germany. The allied representatives agreed on the need to direct the offensive into the heart of the enemy country. It was considered necessary to concentrate forces in such a way as to be able to act either against the enemy forces in East Prussia, or to march on Berlin along the line of operations south of this province, if the concentration of German forces took place on the left bank of the Vistula. Without denying the need for Russia to keep numerous forces against Austria and Sweden, [Gen.] Joffre believed that the defeat of Germany would greatly facilitate the operations of the Russian armies against other enemy powers. It is necessary, therefore, he believed, to strive at all costs to destroy the forces of Germany from the very beginning. To this end, it is necessary to speed up the mobilization and concentration of the allied armies as soon as possible. On the Russian front this can be achieved by the development of railways.
Copies of the original Journals/minutes of the 1912/13 meeting would therefore also be of interest.
[/offtopic]
Part of the conclusion of the articles author (N. Valentinov) was:
At that time, Russia and France faced a probable enemy not only in the person of the Triple Alliance, but also eventually in the person of England. A very troubling period was experienced by the Allies at the end of 1897, when, as a result of complications in Africa, a rift began between France and England. At this time, I had to think about fighting on two fronts against Germany and England, and this was reflected in the negotiations between the Chiefs of Staff, who discussed in the 90s the question of a possible war with England. The tension in relations between Russia and England reached its highest point since the Russo-Japanese War. We will see further how this war affected the application of the convention. From the point of view of the general military situation, in any case, it significantly complicated the position of Russia and France.
However, since 1906, under the influence of King Edward VII, the so-called policy of "encirclement" of Germany begins, caused by the growth of German power and the claims of the Germans to world hegemony. In this regard, there is a rapprochement between France, England and Russia, enshrined in the agreement between France and England on Morocco in 1906 and Russia and England on Persia in 1907.
Sources: