It was New Zealand's first victory of the season after falling short in their two other Cup finals against Samoa in Dubai and Fiji in Australia.
"It was important," coach Gordon Tietjens said of breaking their duck for the season.
"We talked about it just briefly. We had to work really hard. We were quite clinical today. You never underestimate the French either coming into a final like this ... to win it convincingly in the end was awesome."
Series leaders New Zealand scored seven tries to one, Kurt Baker scoring a hat-trick and Ben Lam, Sam Dickson, Tim Mikkelson and Milford Keresoma also dotting down. Tomasi Cama kicked six conversions from seven attempts.
Tietjens' side had edged South Africa 12-5 in the semifinals after thrashing Wales 35-5 in the quarter-finals.
"The players performed magnificently today. The younger players coming in did their bit when they needed to but the core group of five experienced players - Cama, [DJ] Forbes, Mikkelson, [Lote] Raikabula, Baker, they were just outstanding," Tietjens said.
Captain Forbes added: "The boys needed this one - three finals, we needed to start winning. Obviously, looking ahead going into our home tourney, it's good to have one in the bank."
The Wellington tournament will be held on February 1-2.
