The U.S. Constitution, Article 1, Sec.
10 states in part (irrelevant wording removed):
"No state shall enter into any treaty, alliance, or confederation, grant letters of marque or reprisal, emit bills of credit, ..." "No state shall, without consent of Congress, lay any imposts or duties on imports ...
" "No state shall, without consent of Congress, ... enter into any agreement or compact with another state, or with a foreign power ...
"
I cut a lot of the text, but the Constitution makes it clear that an individual state cannot be a party to a treaty or make deals with foreign governments.
California can pass its own emissions caps, carbon credits, etc., but they only apply within the state.
It cannot enforce those provisions outside its jurisdiction, nor can it set up a system of carbon credit swaps with foreign powers or even other U.S. states.
It also can't impose tariffs on imports that don't satisfy environmental limits (although it can tax its own citizens for selling/using them).
There is a lot that California can do on its own to enact some of the provisions of the treaty.
But they are strictly limited in their ability to cooperate with international efforts, and to have their efforts recognized internationally.
FYI:
Letters of marque and reprisal are old English terms for taking actions to sanction another country or state for violating their laws.
A bill of credit refers (in this case) to monetizing carbon credits or some such system of cap and trade that would have the effect of turning them into a tradeable commodity on par with currency.
politics.stackexchange.com/users/9351/Wes Sayeed
Only countries and some international organizations can be parties to international law and treaties, so formally only secession could make California a formal signatory of the Paris Agreement.
Of course, AFAIK, nothing forbids California Governor or Legislature to make a declaration by which they declare to abide by the Paris Agreement and approve the laws and measures needed for this objective, as long as they do not conflict with the Federal powers (the only one that I can think could interfere would be the Commerce Clause).
politics.stackexchange.com/users/6259/SJuan76
The State of California cannot be a signatory or otherwise represent themselves as a separate entity on par with other nations or as anyway act as representing the United Sates, that's a clear violation of the Logan Act, but they could pass similar laws or just voluntarily abide with the agreement.
There is nothing stopping say Leonardo diCaprio from selling his yachts and airplanes and flying coach.
I don't know if that would "differentiate" CA in your estimate.
politics.stackexchange.com/users/9790/K Dog
No, because that's not what "ratify" means.
The details vary from country to country but essentially what happens is that the executive signs the treaty, which says, "I agree that our country should do this, but I need to check with the folks back home.
"
The legislature then gets the chance to ratify the treaty (say "We agree") or not (say "That's crazy talk!
We ain't doin' that!").
So California cannot ratify the treaty for the simple reason that California isn't a signatory.
And California isn't a signatory because foreign relations is the exclusive domain of the federal government.
politics.stackexchange.com/users/4544/David Richerby
Not directly.
The Paris Agreement is a protocol under the United Nations Framework Convention on Climate Change.
The latter is the real treaty.
The reason this formula was chosen, instead of a separate agreement, is to let President Obama bypass Congress.
However, it means that the Paris Agreement can only include parties who already ratified the UNFCCC (Paris Agreement article 20), which California didn't.
That said, ratifying the UNFCCC is also not an option, for the reasons given in other answers.
politics.stackexchange.com/users/10643/MSalters
While not a member of the UN itself, the implementation of  AB 32  effectively satisfies all the requirements of the Paris Agreement.  The state, being so large, contributes to  6.61%  of the US emissions, which is considered  17.89% , or about 1.18% total, replacing Italy as the 18th largest contributor.    So, how could the state peacefully differentiate itself to the UN if the Nation itself decides to not abide to the agreement? Or would it take nothing short of secession?
Could California Ratify the Paris Agreement?
politics.stackexchange.com
<united-states><united-nations><paris-agreement>
politics.stackexchange.com/questions/13481
politics.stackexchange.com/users/10346/Mark
Only countries and some international organizations can be parties to international law and treaties, so formally only secession could make California a formal signatory of the Paris Agreement. The State of California cannot be a signatory or otherwise represent themselves as a separate entity on par with other nations or as anyway act as representing the United Sates - that's a clear violation of the Logan Act - but they could pass similar laws or just voluntarily abide with the agreement.   California is not a signatory thus only secession would work in this instance. 
California is not a signatory. Only secession would work in this instance. 