Ambience and ambiance are different spellings of the same word, referring to the special atmosphere or mood of a particular environment. While some dictionaries list ambiance as the standard spelling, ambience is far more common in all main 21st-century varieties of English. It’s worth noting, though, that ambiance tends to take precedence in contexts relating to art and design, but this is by no means a rule, and exceptions abound.
Ambiance is the French word from which the English one derives, and ambience is an Anglicization. But in fact, the Anglicized word has been in English longer and was established long before the French spelling entered English as a vogue word in the 20th century. So the fact that ambience is more common makes sense, as it has been an English word longer.
Although British English, compared to American English, is usually more welcoming to French words and spellings, most British publications prefer the non-French spelling of ambience, as used in these examples:
The relaxed ambience could also be down to the absence of mobile technology at our table. [Guardian]
Jasper itself is also very popular for skiing, although Jasper Park Lodge doesn’t have the ambience or cachet of the hotels above. [Telegraph]
Canadian, Australian, and American publications also tend to prefer ambience over ambiance:
Parallel lines are encouraged to reflect the nautical ambience. [Montreal Gazette]
In Midtown and Lower Manhattan, we had experienced the ambience and uber-cool of the village life that so attracts people to this unique island. [Herald Sun]
Evidently, too many coffee shops in town have had their ambience wrecked when itinerant word processors with laptops turn the tables into office space. [New York Times]