Tsar Nicholas I did not expect to that two eternal rivals-France and Britain can unite against him. So what should happen to make him right? What is the easiest way to avoid french entry to war? How would Crimean War looks without France?
(bonus if France sides with Russia)
Without France, and their rivalry with Russia over being recognised as 'protector' of Chritsian peoples within the Ottoman Empire (which would hopefully have been enough to prevent a Franco-Russian alliance at that time), there probably wouldn't have been a "Crimean War" as such anyway. Britain would still have opposed the possibility of Russia seizing Constantinople, but I think that they'd have confined their armed support to naval actions -- and maybe helping to garrison the Constantinople area itself, if that became really necessary -- instead of landing troops to try seizing Sebastopol: The disparity in land forces was just too great, otherwise...
Well, either that or they'd have landed a relatively small force to attack Sebastopol quickly -- hopefully taking the garrsion by surprise -- and destroy as many as possible of the Russian navy's facilities there, instead of getting bogged down in a prolonged siege.