Ambience is a nebulous word, refering to the subjective feeling of a place or work of art. It is synonymous with mood, atmosphere, character, or quality.
Ambience has entered the English language twice, and so has two different spellings; in common usage, these two spellings may be treated as exactly the same word. "Ambience", with an 'e', entered written English in 1797, coming to us from the French ambiance, of the same meaning. In 1923 it entered the language again, but this time kept the French spelling, "Ambiance".
Going by dictionary count, 'ambience' is the more common spelling; likewise, UK, Canadian, Australian, and American writers tend to prefer spelling it with an e. This may be changing however, as Google has decided that 'ambiance' is their favorite, and the Chrome spellchecker will red-line you if you try to use the 'e' spelling. I have not been able to find why this is.
Regardless, there is one situation in which it is traditional to use the 'ambiance' spelling; when talking about art and design -- music, painting, interior design, etc. -- it is more common to use the 'a' spelling, most likely because these fields are the ones who keep borrowing the word from the French, and are more aware of the fawncy connotations.