The New Zealanders have won five of six tournaments they have played in this year and are in a pool with Canada, USA and Poland.
The final qualifying spot for next year's Olympic Games is also up for the women's teams. New Zealand, France, Australia and the USA have already qualified, while Ireland, Fiji and Britain are hunting to claim the remaining position. Other sides will face qualifying tournaments.
The All Blacks Sevens can wrap up the HSBC World Series title in Toulouse. They lead by 24 points after their wins in Hong Kong and Singapore, and if they can finish 19 points clear of second-placed Argentina, they could go to the final round next week in London, already the series champions.
They are in a pool with Uruguay, Kenya and Canada.
New Zealand has already qualified for next year's Olympic Games with France; three places are left to be decided in Toulouse and London.
Argentina can qualify by reaching the semifinals in Toulouse, while Fiji could also qualify by winning the Toulouse round.
There is also a race to avoid relegation by the end of the Toulouse round. The 15th-placed side will be relegated, while the sides from 12th-14th will face off with Tonga, the winner of the 2023 Challenger series, for the 12th position for next year's World Series.
Japan is lowest among core teams with 16 points, while Uruguay (49), Spain (48), Kenya (37) and Canada (24) will be looking to lift their points in Toulouse.