Auckland to Amsterdam $944, Paris $986 Return on China Southern Airlines via BYOjet
China Southern Airlines via BYOJet are offering cheap fares to Amsterdam and Paris. The Amsterdam fare is the cheapest ever flight by $55 and the Paris flight is the cheapest ever by $6. Fares include bags, seats and meals. Dates are May & June.
The cheapest fares will have long layovers but for a little more you can avoid big ones. For all stops longer than 8 hours, you'll also get free accommodation. So you could get a very long layover e.g. arrive in Guangzhou at 6AM and leave at midnight so you'll have 18 hours to relax in a hotel or check out the city. Wikitravel: Guangzhou
Find the cheapest dates in Google Flights then plug them into Momondo, Skyscanner or just directly into BYOJet.