The French spell it `ambiance’, while most people in the U.S. spell it `ambience’. As far as the meaning is concerned, there is no difference between the two words.
The `a’ in `ambience’ is like the `a’ in `cat’, act’, and `bat’, while the following `i’ is like the `i’ in `pit’, `bit’, and `fit’. The `e’ in the third syllable sounds like the `a’ in `china’ and the final `e’ is silent. The main stress is on the first syllable. This is one way of pronouncing the word. `Ambience/ambiance’ is normally used to refer to the atmosphere of a place.
*The ambiance/ambience in the new restaurant was fantastic. *The ambience of their new apartment is anything but cosy.
Source: The Hindu ‘Know Your English’ Series, December 5, 2005
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KYE 
Since it is a derivation of a French word, the spelling ought to be with an a.
That would be Cozy, not cosy.
both are correct.