That's interesting - 'vil du ikke' can mean 'will you' or 'won't you', depending on context no doubt.
That's correct GastonDor. The English translation isn't. It should be "Won't you see the new ........".
Since we include "ikke" here, the question becomes negative, meaning that the phrase means "won't" you watch..."
"Vil du se den nye film med mig?"
would that be valid?