On 23 July 1914, the Austro-Hungarian Minister of Foreign Affairs Leopold Count Berchtold (pictured) sent a telegram to the Austro-Hungarian Ambassador to Paris Nikolaus Count Szecsen. In his telegram, Berchtold confirms that the decision to issue the Austro-Hungarian ultimatum to Serbia had little to do with the state visit of the French President to Russia.
Count Berchtold to Count Szecsen. Vienna, 23 July 1914.
As to the coincidence of the démarche [i.e. step] in Belgrade with the departure of [the French President Raymond] Poincaré from Petersburg, it is to be remarked that we always meant to take the démarche as soon as the inquiry in Sarajevo had been concluded. This has since been the case.
It would certainly have been much less amiable to interrupt the festivities in Petersburg by acting at an earlier time, and it would not have been in our interest to undertake our step in Belgrade while Emperor Nicholas and the Russian statesmen were under the influence of the two, who are all for war — Poincaré and [Russian diplomat Alexander Count] Izvolsky.
Source: 1919 Austro-Hungarian Red Book, with minor edits.