The song "Douce Nuit" is "Silent Night". "quiet" can mean "silent", although to me "silent" means "no sound" and "quiet" means "almost silent" - the dictionary says "making little or no noise" for this one. http://www.oxforddictionaries.com/definition/english/quiet http://www.oxforddictionaries.com/definition/english/silent
Most people took the sentence to be talking about the weather of the night being mild or soft. Here in the US, soft could refer to the ambience of the night and mild would be more specifically referring to weather.
You should try reporting it for silent and for quiet which I think could also be accepted.
My preference is for gentle which to me encompasses the surrounding noise, ambience, weather, etc.
There is poetic license for songs, of course. Do they consider it a Good night or a Beautiful night? I think it is both. Here is what happens if you put it into a translator as though it were not the song title: http://www.reverso.net/translationresults.aspx?lang=EN&direction=english-french
Yes, google is not your best translator. "Eau douce" is "fresh water ", "voix douce" is "soft voice ", " "Douce Nuit" " is the song "Silent Night ", "mort douce" is "easy death", "pente douce" is listed as a "flat slope So, I think you get the idea that it depends on which word that it is used with, "gentle, soft" are the most common meanings.
The most common way to say a gentle night is a "mild night", but in some countries they say a "soft night". I would be more likely to say "a gentle slope" and "a gentle death" and I use both "a soft voice" and "a gentle voice". http://dictionary.reverso.net/french-english/douce%20nuit
I don't see why this has to be translated into English with an article. "La nuit est douce" can be a general observation about night in general (or night in a particular place -- "En Hollande, la nuit est douce" = Night is mild in Holland. So I think Duo should accept "Night is mild."