Abdul Hadi Pasha brought to my attention that even very shortly (a few months) before the war the Ottomans did seek an alliance with the French. They felt that they needed to be aligned with one of the two armed camps, lest they should be torn apart by the victors of any great war.
There was a goodly amount of cooperation between Germany and the Ottomans, yet this shouldn't be seen in a vacuum. The RN, as the most highly regarded (rightly or wrongly) naval service,
was seen as the right choice for strengthening the Ottoman Navy. In the event, the French were too wary of upsetting the Russians, the British weren't sufficiently interested (and took the opportunity to snatch more bits of the Empire), and the Germans did not fear upsetting the Russians, and saw the benefit of diverting enemy forces to fight on a broader front.
So you might want to look into the poor old Kaiser making one of his diplomatic faux pas, and the Russians taking the view that if the war does last longer than they hope, then they will need the Straits open. That would not mean the Russians would become closer to the Ottomans, but it might allow the French to act in their interests. The option I went for was to strengthen Anglo-ottoman industrial and business connections, and have the British Army, not the German, called in to oversee the retraining of the Ottoman military. There are problems with this, since it places the British in a position of domination over both land and sea forces, and the British Army wasn't the one anyone went to for bringing their troops up to scratch. So I had to have some slight handwaving, and suggested that behind-the-scenes Franco-Russian influence had made it clear to the Ottomans that getting the Germans in would be regarded disfavourably.
I hope this is of some help to you!