France was complicated - they supported the Turks in the Crimean War, yes, but they also saw themselves as the ones who should protect Christians in the Holy Land. Their choice of Syria and Lebanon as protectorates after WWI wasn't random, they'd wanted those territories for nearly a century beforehand. As for Britain, they'd traditionally defended the Turks from the Russians, but that changed after 1878. There were a few reasons - Liberals like Gladstone were appalled at the atrocities the Turks committed in the Balkans during that war, Conservatives just didn't think they were strong enough to make a worthwhile ally against Russia anyways, and ultimately when they decided to reach an accommodation with France and Russia in the early 00's, they and the French decided that allowing Russia the Straits was worth their cooperation against Germany. There wasn't any interest in protecting the Turks after that, and nobody in either country thought the Empire could be saved regardless, they saw it as an Oriental dinosaur waiting to disintegrate, and they all wanted the best deals they could get out of it. Certainly, if the Italo-Turkish War or Balkan League occurred like OTL, those wouldn't help this impression.
So bottom line, for the Ottoman Empire to survive long-term, you need either a different outcome in 1878, or a different one in 1914. Otherwise, colonizers would keep on knocking at the gates like they had for the past century, only without a British counterbalance anymore.