The legal position is perfectly clear. Syria has a recognised government, that of President Assad, represented at the United Nations. That government is legally entitled to call on Russian military assistance. Russian military action against ISIL is therefore legal.
By contrast, US and French military action has neither the sanction of the Syrian government nor the sanction of the United Nations Security Council. It is therefore plainly illegal.
Neo-con propagandists have attempted in the last fifteen years to promote a new doctrine known as the “responsibility to protect”. This is identical to intellectual justifications of Imperialism from sixteenth century Spain through to Victorian England and Imperial Russia. It holds that misgovernment of less developed nations justifies military action against them by more developed countries out of humanitarian concern. It runs directly to the established international law of non-interference and the need for Security Council sanction of military action. The “responsibility to protect” is not enshrined in any generally accepted international treaty – certainly nothing that overrides the provisions of the UN charter – and is not accepted by the large majority of the countries in the world. It is not customary international law and remains a propaganda phrase, not a legal concept.
Finally, I should add that on precisely the same arguments, Russia’s intervention in Ukraine is, beyond any doubt, illegal.